The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1  1  X  1  1  1  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  X  0  0  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  0  0  X  0  X  X  0  X  X  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  0  0  0  X  X  0  0  0  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  0  X  X  X  X  X  0  0  0  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  0  0  X  0  X  X  0  0  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  X  X  0  X  X  X  0  0  0  0  0  X  0  X
 0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  0  0  X  X  0  X  0  X  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0  X  X  0  X  0  0  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  0  X  X  0  X  0  0  0  0  X  X  X

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+96x^20+328x^24+64x^26+739x^28+640x^30+1225x^32+320x^34+483x^36+168x^40+25x^44+6x^48+1x^52

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 1.02 seconds.