The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+86x^28+74x^29+213x^30+278x^31+377x^32+398x^33+453x^34+550x^35+572x^36+700x^37+657x^38+756x^39+644x^40+644x^41+480x^42+404x^43+298x^44+218x^45+216x^46+54x^47+66x^48+14x^49+25x^50+6x^51+4x^52+1x^54+2x^58+1x^62

The gray image is a linear code over GF(2) with n=76, k=13 and d=28.
This code was found by Heurico 1.16 in 4.39 seconds.