The generator matrix

1 0 0 0 0 0 1 1 1 X 0 1 1 1 1 0 X X 1 1 1 X 0 0 0 X 1 X 1 1 1 1 1 0 0 1 0 X 1 1 0 X 0 1
0 1 0 0 0 0 0 0 0 0 1 1 X+1 1 1 1 1 0 X X 0 1 1 X X 1 X+1 1 X 1 0 0 1 X 1 0 1 1 X 1 1 1 0 0
0 0 1 0 0 0 0 0 0 0 X 0 X 0 X 0 X X X 0 X 0 1 1 1 X+1 1 1 X+1 X+1 1 X+1 X+1 1 X X 1 X+1 0 X X 1 X 1
0 0 0 1 0 0 0 1 1 1 1 0 1 X X+1 X 1 X 0 0 X+1 X+1 1 X+1 1 X+1 X+1 X X 1 X 1 X 0 0 X X X X+1 0 X 1 1 1
0 0 0 0 1 0 1 0 X+1 1 1 1 0 0 X+1 X+1 X 1 0 X+1 X+1 1 X X X+1 1 X X X+1 0 X 1 0 1 1 0 X+1 0 X+1 1 0 1 X+1 X+1
0 0 0 0 0 1 1 X+1 X 1 0 X 0 1 1 1 1 0 0 1 X X 1 0 1 0 X X X+1 X 0 0 X+1 X 1 X 0 0 1 X+1 X+1 X 0 1
0 0 0 0 0 0 X X 0 0 0 0 0 X X 0 0 X X 0 X X X X 0 X 0 X 0 X X 0 0 0 X 0 X 0 X 0 0 0 X X

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+57x^34+134x^35+235x^36+316x^37+386x^38+434x^39+502x^40+532x^41+567x^42+636x^43+604x^44+620x^45+590x^46+556x^47+503x^48+452x^49+351x^50+270x^51+193x^52+120x^53+96x^54+18x^55+10x^56+8x^57+1x^74

The gray image is a linear code over GF(2) with n=88, k=13 and d=34.
This code was found by Heurico 1.10 in 1.81 seconds.