The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  X  1  1  1  0  1  0  0  1  X  1  X  X  0  0  1  1  X  0  0  X  1  1  0  X  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1 X+1  X  1 X+1  1  X  1  X  1  X  1  X  1  1  1  1  1 X+1  1  1  0
 0  0  1  0  0  0  0  0  0 X+1  1  X  1  0 X+1 X+1  X  0  1  X X+1 X+1  X  0  1  0  0  0 X+1  X X+1  X  1 X+1 X+1 X+1  1  0
 0  0  0  1  0  0  0  0 X+1  1  X  X  1 X+1  0 X+1  0  1  X X+1  0  X X+1  1 X+1 X+1  1  0 X+1  0  1  0  0  1 X+1  1  1  0
 0  0  0  0  1  0  0  0  1  0  1  1 X+1 X+1  X X+1  1  X  0  1  X  0  X  X  1  X  X X+1 X+1  X  0  0  1  X  X X+1 X+1  0
 0  0  0  0  0  1  0  1  0  1  0 X+1 X+1  X  0 X+1  1  X  X  0  1  0  X  1 X+1  X X+1 X+1  X  1 X+1  X X+1  1  X  0  0  0
 0  0  0  0  0  0  1  1 X+1  X  1  0 X+1  X  X  1  1  X  1  1  0  1  0 X+1  0 X+1  0 X+1  1  X X+1 X+1 X+1  0 X+1  X  X  0
 0  0  0  0  0  0  0  X  X  0  0  X  0  0  X  X  X  X  X  0  0  0  X  X  X  0  0  0  0  X  0  0  X  X  0  X  0  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+48x^26+156x^27+284x^28+506x^29+696x^30+896x^31+1229x^32+1520x^33+1754x^34+2232x^35+2695x^36+2840x^37+2855x^38+2820x^39+2715x^40+2336x^41+2036x^42+1644x^43+1166x^44+858x^45+590x^46+408x^47+196x^48+128x^49+74x^50+32x^51+31x^52+4x^53+11x^54+4x^55+3x^56

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 71.6 seconds.