The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+152x^12+288x^14+1098x^16+1248x^18+2608x^20+1248x^22+1128x^24+288x^26+120x^28+13x^32

The gray image is a linear code over GF(2) with n=40, k=13 and d=12.
This code was found by Heurico 1.16 in 1.08 seconds.