The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  X  0  X  1  1  1  1  1  1  1  1  1  X  1  X  0
 0  1  0  0  0  1  1  1  0  0  1 X+1  1  0  1  1  X  1  0  0  X  0  1 X+1 X+1  1  1  X  X  1  0
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  X  1  1  1  X  1  0  0 X+1 X+1  0  0  1  1  X  X
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  0  X  X  0 X+1 X+1  X  X  1  1  0  X  1  0  1 X+1  1
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  0  X  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  0  X  X  0  0  X  0  0  X  0  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  X  0  0  X  0  0  X  0  0  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  0  X  X  X  0  X  X  0  0  0  0  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  0  X  0  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  0  0  X  X  0  X  0  X  X  0  0  X  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+175x^20+462x^22+1535x^24+2760x^26+5000x^28+6198x^30+6882x^32+4704x^34+3188x^36+1146x^38+569x^40+88x^42+52x^44+2x^46+5x^48+1x^52

The gray image is a linear code over GF(2) with n=62, k=15 and d=20.
This code was found by Heurico 1.16 in 36.6 seconds.