The generator matrix

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

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+51x^10+68x^11+282x^12+468x^13+750x^14+1148x^15+1932x^16+2808x^17+3213x^18+3632x^19+3876x^20+3936x^21+3332x^22+2464x^23+1836x^24+1416x^25+797x^26+364x^27+258x^28+76x^29+46x^30+4x^31+7x^32+3x^34

The gray image is a linear code over GF(2) with n=40, k=15 and d=10.
This code was found by Heurico 1.16 in 7.76 seconds.