The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  1  X  X  X  X  1  1  1  X  1  X  X  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  X  X  0  0  0  X  0  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  0  0  X  0  X  X  0  X  X  0  X  X  X  0  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  0  X  X  0  X  X  X  0  X  X  0  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0  0  X  X  0  0  X  X  0  0  0  0  X  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  0  X  X  X  0  0  X  X  0  0  0  0  X  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  0  X  0  X  X  0  X  X  0  0  X  0  0  X  0  X
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  0  X  0  0  X  X  0  X  X  X  0  0  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  0  X  0  0  0  X  X  X  0  X  0  0  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  0  X  X  X  X  X  0  0  X  0  X  X  0  X  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  0  0  0  0  0  X  X  0  0  X  X  0  0  X  0  0  X  X

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+112x^28+168x^30+260x^32+433x^34+651x^36+724x^38+656x^40+490x^42+262x^44+142x^46+89x^48+37x^50+15x^52+5x^54+2x^56+1x^70

The gray image is a linear code over GF(2) with n=76, k=12 and d=26.
This code was found by Heurico 1.16 in 1.61 seconds.