The generator matrix

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

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+54x^13+119x^14+164x^15+251x^16+334x^17+400x^18+446x^19+490x^20+534x^21+430x^22+298x^23+260x^24+162x^25+72x^26+50x^27+22x^28+4x^29+3x^30+2x^31

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 2.67 seconds.