The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  0  0  X  1  1  1  1  X  1  0  1  1  0  1  1  1  1  0  1  X  0  0  0  0  X  1
 0  1  0  0  0  0  0  0  0  1  1 X+1  0  X  X  0 X+1 X+1  1  1 X+1  1  X  1  0  1  1 X+1 X+1  1  X  1  1  1  1  X  0  0
 0  0  1  0  0  0  0  0  0  0  1 X+1  1  1  1 X+1  1  0  X X+1  X X+1  1  1  1  1  1  0  1  0  X  X X+1 X+1  1  1  0  0
 0  0  0  1  0  0  0  1  1  1  0 X+1 X+1  X X+1  1  X  0 X+1  0  X X+1  X  1  X X+1  1 X+1  X  X  0  1  X  1 X+1  X  1  0
 0  0  0  0  1  0  1  1  0  1  0  1  X  1  1 X+1 X+1  0  1 X+1  1 X+1  X  0  1 X+1  0  X  1  0  0  1  0  X  X  0  1  0
 0  0  0  0  0  1  1  0  1  1  X X+1  X  1  0  X  X  1  1 X+1 X+1  1  1  0  X  X  1  X  1  1 X+1  0 X+1  1  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  X  0  X  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  0  X  X  X  0  X  0  X  0  0  0  X  X  X  X  0  X  0  X  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  X  X  0  0  0  0  X  X  0  0  X  0  X  0  X  X  0  0  X  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+83x^26+92x^27+348x^28+430x^29+748x^30+848x^31+1232x^32+1522x^33+1879x^34+2204x^35+2483x^36+2968x^37+2736x^38+3176x^39+2576x^40+2364x^41+1993x^42+1500x^43+1226x^44+790x^45+636x^46+360x^47+301x^48+114x^49+109x^50+12x^51+23x^52+4x^53+8x^54+2x^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 56.1 seconds.