The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+36x^21+147x^22+276x^23+422x^24+572x^25+748x^26+1012x^27+1179x^28+1334x^29+1511x^30+1616x^31+1650x^32+1526x^33+1297x^34+1036x^35+737x^36+498x^37+362x^38+196x^39+99x^40+62x^41+31x^42+24x^43+8x^44+4x^45

The gray image is a linear code over GF(2) with n=62, k=14 and d=21.
This code was found by Heurico 1.16 in 23.4 seconds.