The generator matrix

 1  0  0  0  0  1  1  1  1  X  1  1  1  1  1  X  1  0  1  0  1  1  1  0  0  X  1  1  1  1  1
 0  1  0  0  0  X  X  1  X  0  1 X+1  X X+1  0  X X+1  1 X+1  1  1  0  1  0  X  1  0  X X+1  X X+1
 0  0  1  0  0  0  0  0  X  0  X  X X+1 X+1  1  1  1  1 X+1 X+1 X+1  1  0  1  1  X  X  1  X  1  1
 0  0  0  1  0  0 X+1  X X+1  1  1  X  1  0  X X+1  1 X+1  X  0 X+1  0  1  1  X  0  1  1 X+1  X  1
 0  0  0  0  1  1 X+1  1  0  1  1  0  0 X+1  X  1  1  1  X  1  X  1  X  X  1 X+1 X+1 X+1 X+1 X+1  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+152x^26+255x^28+160x^30+114x^32+144x^34+125x^36+56x^38+17x^40

The gray image is a linear code over GF(2) with n=62, k=10 and d=26.
This code was found by Heurico 1.16 in 10.9 seconds.