The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  X  1  X  1  X
 0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  0  X  0  0  0  X  X  0  X  X  0  X  X  X  0
 0  0  X  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  X  0  0  X  0  0  X  X  X  X  X
 0  0  0  X  0  0  0  X  0  X  X  0  0  0  X  X  0  X  0  X  X  X  0  0  X  0  0  X  0  X  X
 0  0  0  0  X  0  0  X  0  X  0  X  0  X  0  X  X  0  X  0  0  0  0  0  X  X  X  0  X  0  X
 0  0  0  0  0  X  0  X  X  0  0  X  0  X  X  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  X  X  X  0  X  0  0  X  0  X  X  X  X  X  X  0  X  X  X  0  X  X  0  0  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+28x^26+53x^28+54x^30+53x^32+38x^34+17x^36+2x^38+2x^40+6x^42+1x^44+1x^52

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 35.4 seconds.