The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  X  X  0  X  0  X  0  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  X  0  0  X  0  0  X  X  0  X
 0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  X  X  0  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  0  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+101x^12+292x^16+256x^18+727x^20+256x^22+340x^24+67x^28+7x^32+1x^36

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 0.0761 seconds.