The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  1  0  1  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  1  1  X X+1  X  0 X+1  1  1
 0  0  1  0  0  0  0  0  1  1  X  1  X X+1  X  X X+1  X X+1  1
 0  0  0  1  0  0  0  0  1  X X+1  1  0 X+1 X+1  1  1  X  0  0
 0  0  0  0  1  0  0  0  1 X+1  1  0  1  X  X X+1  0  1  X  1
 0  0  0  0  0  1  0  1  0  1  X X+1  X  1  1  0  X X+1  1  0
 0  0  0  0  0  0  1  1 X+1  1  0  X  0 X+1  1  1  1  X  0 X+1
 0  0  0  0  0  0  0  X  X  0  0  0  X  X  0  0  0  X  X  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+62x^11+196x^12+436x^13+743x^14+1118x^15+1823x^16+2644x^17+3288x^18+3928x^19+4257x^20+3900x^21+3310x^22+2696x^23+1870x^24+1148x^25+704x^26+378x^27+170x^28+64x^29+19x^30+10x^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 1.11 in 5.22 seconds.