The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1  1  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  0  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X  X  X  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  0  0  X

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+34x^10+102x^12+162x^14+336x^16+804x^18+1164x^20+884x^22+356x^24+122x^26+78x^28+42x^30+11x^32

The gray image is a linear code over GF(2) with n=40, k=12 and d=10.
This code was found by Heurico 1.16 in 0.192 seconds.