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.