The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+40x^13+116x^14+202x^15+251x^16+300x^17+406x^18+502x^19+498x^20+432x^21+411x^22+342x^23+260x^24+188x^25+90x^26+42x^27+14x^28+1x^38

The gray image is a linear code over GF(2) with n=40, k=12 and d=13.
This code was found by an older version of Heurico in 0 seconds.