The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+83x^24+268x^26+364x^28+320x^30+362x^32+302x^34+211x^36+100x^38+34x^40+2x^42+1x^44

The gray image is a linear code over GF(2) with n=62, k=11 and d=24.
This code was found by Heurico 1.16 in 0.194 seconds.