The generator matrix

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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+46x^29+145x^30+246x^31+360x^32+520x^33+631x^34+822x^35+969x^36+1016x^37+1256x^38+1384x^39+1373x^40+1452x^41+1350x^42+1130x^43+1071x^44+880x^45+601x^46+436x^47+279x^48+162x^49+99x^50+72x^51+39x^52+18x^53+14x^54+6x^55+3x^56+2x^57+1x^60

The gray image is a linear code over GF(2) with n=80, k=14 and d=29.
This code was found by Heurico 1.10 in 5.81 seconds.