The generator matrix
1 0 0 0 1 1 1 X 0 1 1 1 1 1 0 X 0 1 0 X 1 1 1 0 1 X 0 1 0 X 0 1 1 1 1 1 1 0 X 1 1 1 0 1 1 X X X X 1 1 1 1 1 0 1 0 0 0
0 1 0 0 0 0 0 0 1 1 1 1 X+1 X 0 1 1 1 0 1 X X+1 X 1 0 1 1 1 1 0 0 X+1 X+1 0 X 1 X+1 X 1 X X X+1 1 X X+1 1 1 1 X X X 0 0 1 0 X X 1 1
0 0 1 0 0 1 1 1 X 1 X+1 X X X+1 X 0 X+1 0 1 1 1 X+1 X 0 0 X+1 X+1 X+1 0 1 0 X+1 X+1 0 1 X+1 X 1 X 0 X X+1 X+1 0 X X 1 X+1 0 1 X+1 X+1 1 X+1 1 X 1 0 X
0 0 0 1 1 1 0 1 1 X X+1 X+1 0 X 1 X 1 0 0 0 X+1 X+1 1 X+1 0 X 1 X X+1 X 1 X+1 1 1 0 0 X X X+1 1 0 X 0 1 X 1 1 X 1 0 X+1 X+1 X X X 0 X 1 X
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 X X 0 X X 0 0 X X 0 X 0 X X 0 0 X 0 X X 0 0 X X X X X 0 X X X 0 X 0
0 0 0 0 0 X 0 0 0 0 0 X X X X X X X 0 0 0 0 X X X X 0 0 X 0 X X X 0 0 X X X 0 X 0 0 0 X X X 0 0 X 0 0 X X X 0 X X X 0
0 0 0 0 0 0 X 0 0 X X 0 0 0 X X 0 X X X 0 0 X 0 X X 0 0 X 0 0 X 0 X 0 0 X X X X X X X 0 X 0 X 0 X X X X X X X 0 X 0 X
generates a code of length 59 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+399x^52+547x^56+535x^60+338x^64+181x^68+41x^72+5x^76+1x^80
The gray image is a linear code over GF(2) with n=118, k=11 and d=52.
This code was found by Heurico 1.16 in 9.6 seconds.