The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+25x^34+42x^35+36x^36+38x^37+30x^38+20x^39+9x^40+16x^41+11x^42+2x^43+5x^44+6x^45+4x^46+2x^48+4x^49+2x^50+3x^52

The gray image is a linear code over GF(2) with n=76, k=8 and d=34.
This code was found by Heurico 1.16 in 0.0103 seconds.