The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  0  0  1  1  X  1  1  0  1  1  X  X  1  1  X  X  X  1  1
 0  1  0  0  0  0  0  0  0  1  1 X+1  0  X X+1 X+1  X  0 X+1  1  X  1  1  X  1  0  X  1  X  X  0
 0  0  1  0  0  0  0  0  0  0  1 X+1  1  1  1  1  1 X+1  X  X X+1  1  X  0  0  X  1  0  X  0  0
 0  0  0  1  0  0  0  1  1  1  0 X+1 X+1  X  1  X X+1  1  X X+1  X  1  X  1  0  0  1  0  1  0  0
 0  0  0  0  1  0  1  1  0  1  0  1  X  1  X X+1  1 X+1 X+1  X  0 X+1  X  1 X+1  X  0  1  0  0  0
 0  0  0  0  0  1  1  0  1  1  X X+1  X  1  X  X  0  X X+1 X+1  1  0 X+1  0  X  X  1  0 X+1  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  0  0  X  0  X  X  0  X  X  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  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+145x^20+692x^22+1531x^24+2946x^26+4675x^28+6242x^30+6418x^32+4944x^34+3011x^36+1396x^38+545x^40+158x^42+57x^44+6x^46+1x^48

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 37.8 seconds.