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 1 0 X 1 X 1 X 1 1 X 1 X 1 1 0 1 0 X 1 0 1 1 X 1 0 1 0 1 1 1 1 0 1 0 X X
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 0 1 0 X 1 X+1 1 0 X+1 0 X 1 0 1 X X X 1 X 0 1 X 1 0 0 X+1 1 1 1 X+1 X+1 0 X+1 1 1 1
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 X 1 0 X+1 0 1 X X 1 1 0 0 0 X 0 1 X+1 X 1 1 X 1 X 1 1 1 X 1 X X+1 1 0 1 0 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 1 X X 0 0 0 0 X+1 1 1 X+1 1 X+1 X+1 0 1 X 1 X X+1 1 0 0 0 X 0 X+1 X+1 1 0 0 X X 1 0 0
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+1 X 0 0 1 1 X 0 1 X X+1 0 0 1 1 X+1 0 X 1 X+1 X X X X+1 X+1 X 1 0 0 1 X+1 1 X 0 X+1 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 0 0 0 X X X X X 0 X X 0 X X X 0 X X 0 0 X 0 0 0 0 0 X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X X 0 0 X 0 0 X 0 X X 0 0 X X 0 0 0 X 0 0 X X X X X X 0 X 0 0 X 0 0 X 0 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 0 X X X X X X X X X X X X X X 0 X X 0 X 0 0 X X X X 0 X 0 X 0
generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 47.
Homogenous weight enumerator: w(x)=1x^0+46x^47+159x^48+212x^49+298x^50+354x^51+395x^52+424x^53+409x^54+506x^55+532x^56+508x^57+471x^58+518x^59+591x^60+524x^61+477x^62+464x^63+354x^64+286x^65+216x^66+140x^67+125x^68+82x^69+40x^70+16x^71+18x^72+10x^73+7x^74+4x^75+1x^76+2x^77+1x^78+1x^86
The gray image is a linear code over GF(2) with n=116, k=13 and d=47.
This code was found by Heurico 1.16 in 8.38 seconds.