The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+22x^29+62x^30+42x^31+104x^32+148x^33+186x^34+108x^35+192x^37+292x^38+192x^39+107x^40+108x^41+172x^42+148x^43+42x^45+30x^46+22x^47+43x^48+26x^50+1x^56

The gray image is a linear code over GF(2) with n=76, k=11 and d=29.
This code was found by Heurico 1.16 in 19 seconds.