The generator matrix

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

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+36x^10+4x^11+100x^12+36x^13+188x^14+208x^15+406x^16+656x^17+776x^18+1144x^19+1032x^20+1144x^21+856x^22+656x^23+416x^24+208x^25+148x^26+36x^27+84x^28+4x^29+44x^30+9x^32

The gray image is a linear code over GF(2) with n=40, k=13 and d=10.
This code was found by Heurico 1.16 in 0.577 seconds.