The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+108x^14+273x^16+392x^18+485x^20+432x^22+254x^24+88x^26+10x^28+4x^30+1x^36

The gray image is a linear code over GF(2) with n=40, k=11 and d=14.
This code was found by Heurico 1.16 in 82.5 seconds.