The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+32x^11+149x^12+276x^13+379x^14+624x^15+946x^16+1296x^17+1614x^18+1828x^19+1964x^20+1936x^21+1708x^22+1260x^23+922x^24+672x^25+370x^26+220x^27+111x^28+44x^29+25x^30+4x^31+3x^32

The gray image is a linear code over GF(2) with n=40, k=14 and d=11.
This code was found by Heurico 1.10 in 1.34 seconds.