The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  0  1  1  1  X  0  1  1  1  0  1  1  X  1  0  1  0  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  1  X  1 X+1 X+1  0  1  1 X+1  0  0  1 X+1 X+1  0 X+1  1  0  1  0 X+1
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  X  X  0  X  0  X  X  X  0  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  0  X  X  X  X  0  0  0  0  X  0  X  0  X  X  0  X  X  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  X  X  0  0  X  X  0  X  X  0  X  0  X  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  X  0  X  0  X  X  X  0  X  0  X  0  0  X  X  X  0  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  X  0  X  0  X  0  0  X  0  X  X  X  0  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  X  0  0  X  0  0  X  0  0  0  X  0  X  X  X  0  X  X  X  X
 0  0  0  0  0  0  0  0  0  X  0  X  0  0  X  X  0  0  X  0  X  X  0  0  0  0  X  0  X  X  0  X  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  X  0  X  X  X  0  X  0  0  0  X  X  0  0  X  X  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+47x^26+6x^27+130x^28+50x^29+186x^30+118x^31+284x^32+370x^33+466x^34+668x^35+583x^36+820x^37+661x^38+876x^39+657x^40+644x^41+453x^42+350x^43+280x^44+154x^45+188x^46+30x^47+96x^48+10x^49+40x^50+15x^52+5x^54+1x^56+2x^58+1x^64

The gray image is a linear code over GF(2) with n=76, k=13 and d=26.
This code was found by Heurico 1.16 in 4.51 seconds.