The generator matrix

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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+104x^34+211x^36+174x^38+135x^40+130x^42+107x^44+90x^46+52x^48+14x^50+6x^52

The gray image is a linear code over GF(2) with n=80, k=10 and d=34.
This code was found by Heurico 1.10 in 0.031 seconds.