The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+119x^26+94x^27+312x^28+318x^29+621x^30+848x^31+1158x^32+1452x^33+1908x^34+2442x^35+2612x^36+2982x^37+2864x^38+3008x^39+2652x^40+2584x^41+1967x^42+1506x^43+1181x^44+762x^45+613x^46+272x^47+235x^48+92x^49+86x^50+22x^51+38x^52+2x^53+14x^54+2x^56+1x^60

The gray image is a linear code over GF(2) with n=76, k=15 and d=26.
This code was found by Heurico 1.16 in 54.4 seconds.