The generator matrix

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

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+60x^11+215x^12+426x^13+689x^14+1178x^15+1849x^16+2528x^17+3362x^18+4044x^19+4121x^20+3852x^21+3420x^22+2672x^23+1828x^24+1184x^25+702x^26+360x^27+175x^28+74x^29+19x^30+6x^31+2x^32+1x^36

The gray image is a linear code over GF(2) with n=40, k=15 and d=11.
This code was found by Heurico 1.16 in 17.3 seconds.