The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 1 1 0 0 0 X 1 1 1 1 1 X 1 0 1 1 1 1 1 1 1
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 1 X+1 0 0 1 1 X+1 1 X X+1 X 0 1 1 X+1 X X X 1 1 1
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 1 1 0 1 0 X X X X+1 1 X+1 X+1 1 X+1 X+1 0 0 1 1
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 X X X X 0 0 0 0 X X X 0 X X X 0 0 X X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 X X X X X 0 X X 0 0 0 0 0 X X X 0 0 X X X 0 X X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 0 X X X X 0 X X 0 X 0 X 0 X X 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X 0 0 X X X 0 X 0 X 0 X X X 0 X 0 0 X
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X 0 0 0 X 0 0 X X X 0 0 X 0 0 X X 0 X 0 X
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X X 0 X X 0 X 0 0 0 X 0 0 0 0 X 0 0 X X
generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+91x^28+52x^29+137x^30+176x^31+195x^32+246x^33+266x^34+348x^35+322x^36+372x^37+347x^38+380x^39+277x^40+296x^41+216x^42+116x^43+115x^44+56x^45+43x^46+4x^47+22x^48+2x^49+14x^50+1x^54+1x^56
The gray image is a linear code over GF(2) with n=74, k=12 and d=28.
This code was found by Heurico 1.16 in 1.11 seconds.