The generator matrix
1 0 0 1 1 1 X 1 1 X 1 X 1 0 1 1 1 1 1 1 X 1 1 0 1 1 1 1 1 1 1 1 1 X 0 1 1
0 1 0 0 1 X+1 1 X X+1 1 0 0 1 1 X X X 0 0 1 1 X X+1 1 0 1 X+1 X+1 X 1 X 1 X+1 1 1 0 X
0 0 1 1 X+1 0 X+1 1 X+1 X X 1 X 1 X+1 X+1 1 1 0 1 X+1 X X+1 X+1 X X+1 0 X X X 0 0 1 1 1 X+1 X
0 0 0 X X X 0 0 0 X X X 0 X X 0 X 0 X X X X X X 0 0 0 X 0 X X 0 0 0 0 0 0
generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+7x^34+32x^35+27x^36+16x^37+18x^38+8x^39+3x^40+5x^42+8x^43+1x^44+1x^46+1x^54
The gray image is a linear code over GF(2) with n=74, k=7 and d=34.
This code was found by Heurico 1.16 in 0.00655 seconds.