The generator matrix

 1  0  0  0  0  1  1  1  1  1  0  X  0  1  1  X  0  1  0  1
 0  1  0  0  0  0  0  0  0  X  X  X  X X+1 X+1  1  1 X+1  1  X
 0  0  1  0  0  1  X  0  1  1  1  1  X  1 X+1 X+1  X X+1  1  1
 0  0  0  1  0  1  0 X+1  1  0  1  X  1 X+1  1  X  X  X X+1  1
 0  0  0  0  1  1 X+1  0  X  X  1 X+1 X+1  0  1  1  0  0  1  1
 0  0  0  0  0  X  X  X  0  X  0  X  X  0  X  0  X  0  0  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+72x^14+88x^15+148x^16+192x^17+183x^18+216x^19+210x^20+256x^21+206x^22+200x^23+138x^24+64x^25+48x^26+8x^27+14x^28+2x^30+1x^32+1x^34

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 0.118 seconds.