The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+16x^26+26x^27+34x^28+34x^29+22x^30+20x^31+15x^32+20x^33+14x^34+18x^35+12x^36+10x^37+10x^38+2x^42+2x^44

The gray image is a linear code over GF(2) with n=62, k=8 and d=26.
This code was found by Heurico 1.16 in 0.015 seconds.