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.