The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 0 1 1 X 1 0 1 1 X 1 1 1 1 0 1 1 X 1 1 1 1 0 1 0 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 X 1 X 1 0 1 1 X 1 1 1 1 1 0 1 1 X 1 1 1 0 X 0 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1
0 1 1 0 1 1 0 1 1 X X+1 1 0 X+1 1 X+1 1 0 X+1 1 0 1 X+1 0 1 X+1 X 0 X+1 1 0 X+1 1 X X X+1 1 1 1 1 0 1 X+1 1 1 0 X+1 0 0 X+1 X 0 X+1 1 X+1 1 1 1 X+1 1 X 1 X+1 1 X X 1 1 0 X X 1 1 X 0 1 X+1 0 1 1 1 1 X+1 1 1 1 1 X 0 X X+1 0 1 X 1 0 X+1 X+1
0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X X X X 0 X 0 X X 0 X 0 X X 0 0 X X X X 0 X X 0 X X X 0 X 0 X X 0 0 0 0 0 0 X X X X X 0 0 0 0 0 0 0 0 0 0 0 X X
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 X X 0 X X X X 0 X 0 X X X X X X 0 0 X X 0 X 0 X X 0 0 X 0 0 0 X 0 X 0 X X X 0 0 0 0 X 0 0 0 0 X 0 X X X X 0 X 0 X 0 0 X X 0 0 0 X X 0 0 X X 0 0 0 X 0 0 0 0 X 0 0 X X
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X X 0 X X X X 0 0 0 0 0 X X X 0 X X 0 X X 0 0 0 X 0 X 0 X 0 X 0 0 X X 0 0 0 X 0 0 X 0 0 0 0 X X X 0 0 X X 0 X 0 0 X 0 X X 0 X X 0 X X X 0 0 0 0 X 0 X X X X X X 0
0 0 0 0 0 X 0 0 0 0 0 X 0 X X X 0 0 0 X 0 0 X 0 X 0 0 X X X X X X X X 0 0 0 X X X X 0 X 0 X X 0 X 0 0 X X X X 0 0 0 0 X X 0 0 X X X 0 0 0 0 0 X X X X 0 X X X X X 0 X 0 X X 0 X X X 0 0 X 0 X X 0 X
0 0 0 0 0 0 X 0 0 X 0 0 X X 0 X 0 0 0 0 0 0 X X 0 0 X 0 X X X X X X 0 X 0 X X X X X 0 X 0 X 0 0 0 0 X 0 0 0 0 X X X 0 0 X 0 X 0 0 X 0 X X X 0 0 0 X X X X X X X 0 X 0 X 0 X X 0 X 0 0 0 0 0 0 0 X X
0 0 0 0 0 0 0 X 0 0 X 0 X 0 0 X 0 X X 0 0 X X 0 X X X X X 0 0 X X X 0 0 X 0 0 0 X 0 0 X X 0 X 0 0 0 0 0 0 X X X 0 0 0 0 0 X X X X X X X 0 0 X X X 0 X X 0 X 0 0 0 0 X 0 X 0 0 X X X 0 X X X 0 0 X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 X 0 0 X X X 0 X 0 X 0 X X X 0 X X 0 0 0 0 X X X X 0 X X 0 0 X X 0 0 0 X X X X 0 0 X X X 0 0 X X 0 0 X X X 0 X 0 X 0 0 0 0 0 0 0 X X X X 0 0 0 X 0 0 0 X 0 X 0 0 0 X X 0 0
generates a code of length 98 over Z2[X]/(X^2) who´s minimum homogenous weight is 88.
Homogenous weight enumerator: w(x)=1x^0+145x^88+152x^90+288x^92+156x^94+261x^96+148x^98+217x^100+188x^102+208x^104+100x^106+98x^108+24x^110+29x^112+14x^116+10x^120+6x^124+1x^128+1x^132+1x^136
The gray image is a linear code over GF(2) with n=196, k=11 and d=88.
This code was found by Heurico 1.16 in 1.48 seconds.