The generator matrix

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

generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+8x^21+50x^22+170x^23+299x^24+416x^25+572x^26+750x^27+961x^28+1218x^29+1341x^30+1452x^31+1596x^32+1544x^33+1521x^34+1376x^35+1042x^36+750x^37+525x^38+370x^39+180x^40+86x^41+87x^42+42x^43+16x^44+8x^45+2x^49+1x^52

The gray image is a linear code over GF(2) with n=64, k=14 and d=21.
This code was found by an older version of Heurico in 0 seconds.