The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+179x^12+792x^14+1837x^16+3130x^18+4352x^20+3442x^22+1736x^24+686x^26+213x^28+14x^30+2x^32

The gray image is a linear code over GF(2) with n=40, k=14 and d=12.
This code was found by an older version of Heurico in 0 seconds.