The generator matrix

1 0 0 0 0 1 1 1 1 1 0 0 X 1 1 X X 1 0 1
0 1 0 0 0 0 0 0 0 X X X X 1 X+1 1 1 1 1 1
0 0 1 0 0 1 0 1 X 1 1 1 0 1 X+1 1 0 X+1 X+1 1
0 0 0 1 0 1 0 X+1 1 0 1 X 1 X+1 X+1 X X X 1 1
0 0 0 0 1 1 X+1 X 1 X+1 1 X+1 X+1 X+1 X 1 0 X+1 X+1 0
0 0 0 0 0 X X 0 0 0 0 X X X 0 0 X 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+93x^14+319x^16+369x^18+458x^20+426x^22+296x^24+70x^26+14x^28+1x^30+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 1.10 in 0.031 seconds.