The generator matrix

 1  0  1  1  1  0  1  1  1  1  0  0  X  0  0  X  1  0  1  0
 0  1  1  0  1  1  0  1  X X+1  1  1  1  1  1  1  0  1 X+1  1
 0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  0  X
 0  0  0  X  0  0  0  0  X  0  0  X  X  X  X  0  0  0  X  X
 0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  0  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  0  0  0  X  X  0  X
 0  0  0  0  0  0  X  0  X  0  X  X  0  0  X  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  X  X  X  0  X  0  X  0  X  0  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+48x^14+89x^16+128x^17+68x^18+128x^19+85x^20+128x^21+108x^22+128x^23+70x^24+28x^26+10x^28+4x^30+1x^36

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 1.48 seconds.