The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  X  1  1  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  1  X  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  X  0  0  X  0  X  X  0  X  X  X
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  X  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  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+57x^12+30x^14+355x^16+260x^18+582x^20+416x^22+230x^24+60x^26+49x^28+2x^30+6x^32

The gray image is a linear code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in 0.0633 seconds.