The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  X  0  1  1  0  0  1  X  0  1  X  1  X  0  1  1  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  X X+1  X  X  X  1 X+1  1  1 X+1  1  0  1  0
 0  0  1  0  0  0  0  0  0  1  1  1  1  1  X  0  X  X X+1  1  1  X  0  1  0 X+1 X+1 X+1  X  1  0
 0  0  0  1  0  0  0  0  1  0 X+1  X  1 X+1 X+1  1  0  1  1  0  1  X  X  X  1 X+1  X  X X+1 X+1  0
 0  0  0  0  1  0  0  0  1  1  0  X X+1  X  X X+1 X+1  0  0  X  0 X+1  1  1  1  1  X  0  X X+1  0
 0  0  0  0  0  1  0  1  0 X+1 X+1  X X+1  1  X  1  1 X+1 X+1  1 X+1 X+1 X+1  0  X  1 X+1 X+1  0  1  0
 0  0  0  0  0  0  1  1 X+1  X  0  1  1 X+1  0  1  0  X  1  0  X  0  1  0 X+1  1 X+1  X X+1 X+1  0
 0  0  0  0  0  0  0  X  X  0  X  0  X  0  X  0  X  X  X  X  0  X  0  X  X  X  0  X  0  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+114x^20+98x^21+375x^22+478x^23+929x^24+1072x^25+1494x^26+1836x^27+2393x^28+2878x^29+2703x^30+3450x^31+3109x^32+3100x^33+2452x^34+2028x^35+1532x^36+938x^37+773x^38+374x^39+345x^40+100x^41+134x^42+24x^43+25x^44+6x^45+5x^46+2x^47

The gray image is a linear code over GF(2) with n=62, k=15 and d=20.
This code was found by Heurico 1.11 in 16.7 seconds.