The generator matrix

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

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+53x^34+71x^36+41x^38+41x^40+25x^42+13x^44+3x^46+2x^48+4x^50+2x^58

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 18 seconds.