The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+63x^10+188x^11+381x^12+776x^13+1381x^14+2348x^15+3629x^16+5128x^17+6726x^18+7856x^19+8274x^20+7896x^21+6778x^22+5296x^23+3806x^24+2456x^25+1387x^26+692x^27+289x^28+128x^29+49x^30+4x^31+4x^32

The gray image is a linear code over GF(2) with n=40, k=16 and d=10.
This code was found by Heurico 1.11 in 16.2 seconds.