The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+46x^13+115x^14+196x^15+251x^16+298x^17+412x^18+480x^19+485x^20+458x^21+421x^22+372x^23+271x^24+150x^25+71x^26+40x^27+15x^28+8x^29+4x^30+1x^32+1x^34

The gray image is a linear code over GF(2) with n=40, k=12 and d=13.
This code was found by Heurico 1.16 in 0.324 seconds.