The generator matrix

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

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+182x^26+192x^28+168x^30+151x^32+160x^34+88x^36+64x^38+16x^40+2x^42

The gray image is a linear code over GF(2) with n=62, k=10 and d=26.
This code was found by Heurico 1.10 in 68.1 seconds.