The generator matrix

 1  0  0  0  0  0  1  1  1  X  0  1  1  1  1  0  X  1  0  0  X  1  1  1  X  1  1  0  1  1  1  0  X  1  1  X  0  1
 0  1  0  0  0  0  0  0  0  0  1  1  1  1 X+1  1  1  0  X  X  1  0  X  0  1 X+1  1  X  1  X X+1  0  1  X  X  0  0 X+1
 0  0  1  0  0  0  0  0  0  0  X  0  X  0  X  0  X  X  X  0  1 X+1  1 X+1 X+1 X+1  1  1  1  1  1  0 X+1 X+1 X+1  1  1  1
 0  0  0  1  0  0  0  1  1  1 X+1  1  0 X+1  X  X  1  0  1  1 X+1  X  X  1  1  X  X  1  0  1  1  1  1  0  0  X  1 X+1
 0  0  0  0  1  0  1  1  X X+1  1  0 X+1 X+1  0  1  X  1  0 X+1  X  1  0 X+1  1  0 X+1  X  X  X X+1  1  1  X  X X+1 X+1  1
 0  0  0  0  0  1  1  X X+1  1  0  0  X  1 X+1  1  1  1  0  1  1  0 X+1 X+1 X+1  X  1 X+1  0  0  X  0  X  0  X  X  X  1
 0  0  0  0  0  0  X  0  X  0  0  X  X  X  X  X  X  0  X  X  0  0  0  0  X  0  0  0  0  X  0  X  0  X  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+102x^29+235x^30+278x^31+343x^32+422x^33+530x^34+538x^35+573x^36+680x^37+696x^38+716x^39+664x^40+600x^41+536x^42+420x^43+278x^44+226x^45+172x^46+94x^47+56x^48+18x^49+6x^50+2x^51+5x^52+1x^62

The gray image is a linear code over GF(2) with n=76, k=13 and d=29.
This code was found by Heurico 1.16 in 33.2 seconds.