The generator matrix

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

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+40x^14+142x^16+220x^18+232x^20+212x^22+128x^24+36x^26+8x^28+4x^30+1x^32

The gray image is a linear code over GF(2) with n=40, k=10 and d=14.
This code was found by Heurico 1.16 in 0.0237 seconds.