The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 X 1 1 1 1 0 1 X 1 1 1 0 1 1 1 0 0 1 X X 1 1 0 1 1 1 0 X 1 0 X 1
0 1 1 0 1 1 0 1 1 X X+1 1 1 0 X+1 0 X+1 1 X+1 1 X 0 X+1 1 X+1 1 0 1 1 X+1 1 1 0 X 1 0 X X 1 1 X X 0 0
0 0 X 0 0 0 0 0 0 0 X 0 0 X X X X 0 0 0 0 X X X X 0 0 0 X X X 0 0 X X X X 0 0 X 0 0 X 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 X X 0 X X X X X X X X X X X X X 0 0 0 X X 0 X X X X 0 X X 0
0 0 0 0 X 0 0 0 0 0 X X X X 0 X X X X X 0 X X X 0 0 0 0 0 0 X 0 X X 0 0 0 X 0 0 X 0 0 0
0 0 0 0 0 X 0 0 X 0 0 X 0 X 0 X 0 X 0 0 0 X X X X 0 X X 0 X X X 0 0 0 0 X X 0 0 0 X 0 0
0 0 0 0 0 0 X 0 X X 0 0 X X 0 0 X 0 X 0 X X X X 0 0 0 X 0 0 X X 0 X 0 X X 0 0 X X X 0 X
0 0 0 0 0 0 0 X X 0 X 0 X X X 0 0 X 0 X X X 0 X X X 0 X 0 0 X 0 X X X X 0 0 0 0 X 0 X X
generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+25x^36+24x^37+64x^38+52x^39+78x^40+108x^41+77x^42+92x^43+61x^44+68x^45+63x^46+76x^47+58x^48+52x^49+34x^50+36x^51+23x^52+4x^53+14x^54+6x^56+1x^58+3x^60+3x^62+1x^64
The gray image is a linear code over GF(2) with n=88, k=10 and d=36.
This code was found by Heurico 1.16 in 0.112 seconds.