The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  X  0  0  0  X  1  1  1  X  0  1  X  1  1  X  1  1  X  1  1  0  0  1  X  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  1  1  1  1 X+1  1  1  1  X  1 X+1  1  X X+1  X  X  1  0  0  0
 0  0  1  0  0  0  0  0  0  1  1  1  1  1  X  0  X  X  X X+1 X+1  0 X+1  X X+1  X  0  X X+1 X+1 X+1  0  1  X  X  1  1  0
 0  0  0  1  0  0  0  0  1  0 X+1  X  1 X+1  0  1  1 X+1  X  1 X+1  X X+1 X+1  0  X  1 X+1  1  0 X+1  0 X+1  0 X+1  X  0  0
 0  0  0  0  1  0  0  0  1  1  0  X X+1  X  1  X  1  1  1  0  0 X+1  0  X  X  X  1  0 X+1 X+1  X X+1  0  0  1  1  1  0
 0  0  0  0  0  1  0  1  0 X+1 X+1  X X+1  1 X+1 X+1  1  0  X  0  X  0 X+1 X+1  1  0 X+1  0  1 X+1  X  0 X+1  1 X+1  0  0  0
 0  0  0  0  0  0  1  1 X+1  X  0  1  1 X+1  0  X  1  0  0  X  1 X+1 X+1  X  1 X+1  X X+1  1  0 X+1 X+1  0  1  X  0  1  0
 0  0  0  0  0  0  0  X  X  0  X  0  X  0  X  X  0  0  X  0  X  X  X  0  X  X  0  0  X  X  X  0  0  0  X  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+93x^26+90x^27+369x^28+400x^29+683x^30+886x^31+1248x^32+1532x^33+1875x^34+2292x^35+2517x^36+2886x^37+2742x^38+3010x^39+2554x^40+2446x^41+1992x^42+1604x^43+1211x^44+818x^45+711x^46+284x^47+249x^48+110x^49+87x^50+22x^51+39x^52+8x^54+4x^55+4x^56+1x^58

The gray image is a linear code over GF(2) with n=76, k=15 and d=26.
This code was found by Heurico 1.11 in 24.7 seconds.