The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 X X X X 0 1 1 0 0 1 X 1 0 1 X 1 1 0 1 X 1 X 0 X 1 0 X X
0 1 0 0 0 1 1 1 0 0 1 X+1 1 0 1 1 X 0 0 1 1 X X 1 X 1 1 X+1 0 1 1 1 X 1 0 X X 0 1 0
0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 X 1 X+1 0 X 1 0 X X+1 1 1 1 0 1 0 X 0 1 X+1 1 1 0 1 X+1 0
0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 X X 1 1 1 X+1 X 1 X 1 X+1 0 1 X 0 1 X+1 1 0 0 X+1 1 X X+1 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X X 0 0 X 0 0 0 X 0 0 X 0 X X 0 X X
0 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X X 0 0 0 X X X 0 0 X X X X 0 0 X 0 X X X 0 X X
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X X 0 X X X 0 0 0 X X 0 X X X 0 0 X X X 0 0 0 0 X 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X 0 X 0 0 X X 0 X 0 0 X X 0 0 X 0 0 0 X 0 X X 0 0
0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X X X 0 X 0 0 0 X X X 0 0
0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X 0 X 0 X X X X X 0 0 X 0 0 0 0 0 X X 0 0 0 0
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 0 0 X 0 X X X X X X X X X X X 0 X X X 0
generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+213x^28+502x^30+1452x^32+2128x^34+4024x^36+5006x^38+6011x^40+5056x^42+4122x^44+2274x^46+1335x^48+368x^50+216x^52+26x^54+33x^56+1x^60
The gray image is a linear code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.16 in 60 seconds.