The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+67x^20+26x^22+276x^24+248x^26+705x^28+668x^30+880x^32+504x^34+469x^36+90x^38+135x^40+23x^44+3x^48+1x^56

The gray image is a linear code over GF(2) with n=62, k=12 and d=20.
This code was found by Heurico 1.16 in 0.785 seconds.