The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 1 X 1 1 X 0 1 X 0 X 1 1 1 0 0 1 1 X 1 0 1 0 1 X X 1 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 0 1 X 0 1 1 X+1 1 1 X 0 1 0 X 1 1 1 X 1 0 1 1 X+1 0 X 0 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 1 X 0 X+1 X 1 X 1 1 0 X 1 X+1 1 X+1 0 X 0 0 X 0 0 1 X X
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 1 0 X 0 0 0 X 0 0 1 0 X+1 1 1 X+1 X 0 1 0 X X+1 X 1 1 X+1 0 1
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 X+1 1 X 1 X+1 X 0 0 X+1 0 X X+1 0 X+1 X 1 1 1 X 1 1 X+1 0 0 X 1 X+1
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X X X X 0 X X X X X 0 X X X 0 0 X X X 0 0 0 0 X X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X X 0 0 X X 0 X 0 0 X 0 X X X X 0 X X 0 0 0 X 0 X 0 X X
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X 0 X X X X X 0 0 X X X 0 X
generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+217x^42+522x^44+730x^46+1015x^48+1079x^50+1144x^52+1022x^54+1023x^56+719x^58+452x^60+182x^62+64x^64+17x^66+1x^68+2x^70+1x^72+1x^84
The gray image is a linear code over GF(2) with n=104, k=13 and d=42.
This code was found by Heurico 1.16 in 7.84 seconds.