The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  X  1  1  1  X  0  0  0  0  1  X  X  1  0  1  0  1  X  1  1  1  X  X  0  X  0  X  1  1  0  0  1  1  1  1  1  X  0  1  1  1  1  1  0  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  1  1  1  1  1  1 X+1  1  1  1  0  1  1  X  1  X  X  1  1  1 X+1  0  1  X  0  1  0 X+1  X  1  0  1 X+1  0 X+1  1  X  0  0
 0  0  1  0  0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  X  X X+1  0  1  X X+1 X+1 X+1  1  1  X  0  1 X+1  X  0  1 X+1  X  0  X X+1 X+1  1  0  0 X+1  1  1  X  1  X  1  X  1  1  1  0
 0  0  0  1  0  0  0  0  1  1  0  1  X  0  1 X+1  0  X  1  1  X X+1  1  0  1  X  X  1  0 X+1 X+1  X  X X+1  1  0  X  0  1  X  1  0  0  1  1  0 X+1  0 X+1  X  X  1  0  0  0 X+1  0  0
 0  0  0  0  1  0  0  0  1  X  1 X+1  X  0  1  X  X  1  1  1  1  X X+1 X+1 X+1 X+1 X+1  0  0  1  1 X+1  1  1 X+1  1  0  1  0  0  0 X+1 X+1  X  X X+1 X+1  1  0  0 X+1  0  X  0  X  X  0  0
 0  0  0  0  0  1  0  1  0  1 X+1 X+1  X  1  0  X  1  0 X+1  X  1  1 X+1  1  X  0  1  0  0  1 X+1  X  1  X  0 X+1  X  X  1  0 X+1  1 X+1  X  1  0  X  1  X X+1  0  0  1  1 X+1  1  0  0
 0  0  0  0  0  0  1  1 X+1  0  X  1  1  X  X X+1  1  1  X  0  1  0  0  0  1  1  1  0  0  X X+1 X+1  X  X X+1  0  1  1  X  X  X  0 X+1 X+1  1  X  1 X+1  1  X  0 X+1  1 X+1 X+1 X+1  X  0
 0  0  0  0  0  0  0  X  X  0  0  X  X  0  0  X  X  X  0  0  X  0  0  0  X  X  X  0  X  X  0  0  X  X  0  X  0  0  X  0  X  X  0  0  0  X  0  0  X  X  0  X  0  0  0  0  X  0

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+83x^44+110x^45+255x^46+380x^47+612x^48+668x^49+953x^50+1074x^51+1321x^52+1542x^53+1766x^54+2038x^55+2023x^56+2190x^57+2199x^58+2532x^59+2170x^60+2092x^61+1892x^62+1704x^63+1358x^64+1018x^65+878x^66+602x^67+489x^68+270x^69+218x^70+102x^71+125x^72+42x^73+23x^74+16x^75+9x^76+2x^77+5x^78+1x^80+2x^81+3x^82

The gray image is a linear code over GF(2) with n=116, k=15 and d=44.
This code was found by Heurico 1.11 in 47.3 seconds.