The generator matrix
1 0 0 0 1 1 1 1 0 1 0 1 1 X 0 X X 0 0
0 1 0 0 0 0 1 1 1 X 1 1 X 0 0 1 1 1 1
0 0 1 0 0 1 1 0 X+1 1 X X+1 0 1 1 0 X X+1 X+1
0 0 0 1 1 1 0 X+1 X+1 0 1 X+1 X+1 1 0 X 1 X+1 0
0 0 0 0 X 0 0 0 0 X X X X 0 X 0 X X 0
0 0 0 0 0 X 0 X 0 X 0 0 X X 0 0 X X X
0 0 0 0 0 0 X X X 0 0 0 X X 0 X 0 X 0
generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.
Homogenous weight enumerator: w(x)=1x^0+46x^13+111x^14+134x^15+188x^16+206x^17+210x^18+246x^19+230x^20+218x^21+176x^22+130x^23+90x^24+42x^25+14x^26+2x^27+2x^28+1x^30+1x^32
The gray image is a linear code over GF(2) with n=38, k=11 and d=13.
This code was found by Heurico 1.16 in 18.9 seconds.