The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  0  1  1  0  X  0  X  X  0  1
 0  1  0  0  0  1  1  1  0  0  1 X+1  1  1  X  1  1  X  0  0  1  1  0  1  0 X+1
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  X X+1  1  1  0  1  X  1 X+1  0  X
 0  0  0  1  1  0  1  1  1  0  1  0  1  X X+1 X+1 X+1  X  1  1  0  1  1  1  1  X
 0  0  0  0  X  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X  0  X  0  X  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0  X  0  X  X  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  X  0  X  X  X  X  X  X  0  0  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  X  0  0  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  0  X
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  0  0  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  0  0  X  0  X  0  X  0  X

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+217x^16+598x^18+1895x^20+3574x^22+6695x^24+6924x^26+6387x^28+3772x^30+2002x^32+478x^34+197x^36+14x^38+13x^40+1x^44

The gray image is a linear code over GF(2) with n=52, k=15 and d=16.
This code was found by Heurico 1.16 in 23.4 seconds.