The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X 1 X 1 1 X 1 X X 1 1 X 1 X 1 X X 0 1 0 X 1 0 0 1 1 0 1 1 1 1 0 1 X 1 1 X 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X 0 X 0 0 0 X X X 0 X X X 0 X 0 X X 0 X 0 X 0 X X X 0 0 X 0 0 X 0 X 0 X X 0 0 0 X 0 0 0 0 0 0 0 X X 0 0 X X 0 X X 0 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 0 0 X X X 0 0 0 X X X 0 X X 0 0 X X X 0 0 0 X X X 0 0 0 X X X X X 0 0 0 0 0 X X 0 0 X X 0 0 0 X 0 0 X 0 0 X 0 0 0 0 X X X 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X X 0 X 0 0 X X 0 0 0 X X X 0 X 0 X X 0 0 X X X 0 0 0 0 0 X X 0 X X 0 0 X 0 0 X X X X 0 0 X X X X X 0 X 0 0 0 0 X 0 X X 0 X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X X X X X 0 X X 0 0 0 X 0 0 0 0 X 0 X 0 X 0 X X X 0 X X 0 X 0 0 X X X 0 X 0 0 X X 0 X X X 0 0 X X X 0 X 0 X 0 0 0 0 X X X 0 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 X X 0 0 0 X 0 X 0 0 0 0 X X 0 X X X 0 0 0 X X X 0 0 0 0 X 0 0 0 X X 0 X X X 0 0 X 0 0 0 X X X X X 0 0 X X 0 X 0 0 0 0 0 X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 0 X X X 0 0 0 0 X 0 0 0 X X X X 0 X X X X X 0 X 0 X X X X 0 X 0 0 X 0 X X 0 X X X X X 0 X X X X 0 0 0 0 0 X X 0 0 X 0 0 0 0 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X X X X 0 0 0 X X X X X 0 0 0 0 X X X X X 0 0 X 0 0 0 X X X 0 X X 0 X 0 X X 0 X X X X X X 0 0 0 X 0 X 0 0 X 0 0 X 0 0 X X 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X 0 X X X X 0 0 0 X X X X 0 X 0 0 0 0 X 0 0 0 X 0 X X X 0 X 0 0 0 X 0 0 X X X X X X X 0 0 0 0 X X 0 X X X X X 0 0 0 X X
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 0 X X 0 X X 0 0 0 0 X 0 0 0 X 0 X X 0 0 X X X X X X 0 0 X X X X 0 X X X 0 X X 0 0 X X X X X 0 X X 0 0 0 0 X X 0 X 0 0 X 0 0 X
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 X 0 X 0 0 X 0 X X 0 0 0 X 0 0 X 0 0 X X 0 X 0 X X X X 0 0 X X X 0 X 0 0 0 0 X 0 X 0 X 0 0 0 0 X X X 0 0 X X X 0 X X 0 0 0 X 0
generates a code of length 94 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.
Homogenous weight enumerator: w(x)=1x^0+40x^78+92x^80+10x^81+141x^82+32x^83+135x^84+70x^85+151x^86+106x^87+167x^88+166x^89+141x^90+296x^91+144x^92+358x^93+135x^94+318x^95+138x^96+278x^97+130x^98+208x^99+128x^100+114x^101+105x^102+54x^103+96x^104+26x^105+87x^106+8x^107+73x^108+2x^109+61x^110+2x^111+31x^112+27x^114+15x^116+2x^118+3x^120+2x^122+1x^124+1x^126+1x^142
The gray image is a linear code over GF(2) with n=188, k=12 and d=78.
This code was found by Heurico 1.16 in 7.03 seconds.