The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 X X X X 0 X 1 0 1 1 1 1 0 1 1 1 X 1 X 0 1 1 1 X 1 1 X X 1
0 1 0 0 0 1 1 1 0 0 1 X+1 1 0 1 1 X 1 0 1 X 0 1 X+1 0 X+1 1 1 X X 0 1 0 0 X+1 1 0 1 0 0 0
0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 X 1 1 1 0 X+1 X 0 1 0 X X+1 X+1 1 1 1 0 0 X 1 X+1 X 0 X 0 0
0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 X X 0 X+1 X+1 0 X+1 X+1 0 1 0 X X+1 1 X 0 0 X+1 X 1 1 X+1 X+1 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 X X 0 X 0 0 X X X X 0 0 X X X 0 0 X X X X 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X 0 X X 0 X 0 X X X X X X X 0 0 0 X 0 0 X 0 0 X 0
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X X 0 X 0 X X 0 X 0 X 0 X X 0 0 X 0 X 0 X X X X X X 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X 0 X X 0 0 X 0 0 0 0 X X X X 0 X X 0 0 X X 0 X 0 0
0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 0 X X X 0 X X 0 X 0 X X X 0 0 X X X X 0 X X 0
0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X X X 0 0 X 0 X X 0 X X X 0 0 0 0 0 0 X X X 0 0
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X 0 X X 0 0 0 X X X X X 0 0 X 0 0 X X 0 X X X X
generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+76x^28+74x^29+231x^30+278x^31+476x^32+670x^33+936x^34+1162x^35+1560x^36+1888x^37+2198x^38+2684x^39+2686x^40+2880x^41+2720x^42+2596x^43+2233x^44+1978x^45+1587x^46+1214x^47+949x^48+638x^49+445x^50+242x^51+178x^52+60x^53+64x^54+16x^55+32x^56+4x^57+10x^58+1x^60+1x^66
The gray image is a linear code over GF(2) with n=82, k=15 and d=28.
This code was found by Heurico 1.16 in 58.9 seconds.