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.