The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  X  1  1  1  1  1  0  1  1  0  0  X  1  1  0  X  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  1  1 X+1  X  1  X  1  1  1  1  X X+1  1  1 X+1  1  0
 0  0  1  0  0  0  0  0  0 X+1  1  X  1  0  0 X+1 X+1  1 X+1 X+1  X  0  1 X+1 X+1 X+1 X+1  1  0  1  0
 0  0  0  1  0  0  0  0 X+1  1  X  X  1 X+1  1  X X+1  0  0  X  X  X  X  1  0 X+1  1  X  X  0  0
 0  0  0  0  1  0  0  0  1  0  1  1 X+1 X+1  X  X  0  1  X  1  0  X  0  0  1  1 X+1  1  1  1  0
 0  0  0  0  0  1  0  1  0  1  0 X+1 X+1  X  X X+1 X+1 X+1  1  X X+1  1  0 X+1  1  1 X+1  X  0  1  0
 0  0  0  0  0  0  1  1 X+1  X  1  0 X+1  X  X  X  1  X X+1  0  1 X+1 X+1 X+1  1  1  X X+1  1  1  0
 0  0  0  0  0  0  0  X  X  0  0  X  0  0  X  0  X  0  0  X  0  X  0  X  0  X  0  X  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+103x^20+102x^21+446x^22+456x^23+814x^24+1102x^25+1548x^26+1798x^27+2340x^28+2922x^29+2824x^30+3502x^31+3055x^32+2998x^33+2440x^34+2026x^35+1495x^36+964x^37+822x^38+386x^39+346x^40+100x^41+108x^42+24x^43+38x^44+4x^45+4x^46

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 44.5 seconds.