The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^2  0  0  X  1  1  X  0  1  X  0  X  1  X  1  1  0  0  1 X^2  1  1 X^2  X  X  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2 X^2  0  X X^2 X^2+X  X  0 X^2 X^2  X  0  X X^2+X X^2 X^2+X  0 X^2  X  X X^2 X^2  X  0 X^2+X  X X^2  X  X  X  0  X  0  X  0  0  X  X  X X^2 X^2  X  X  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0  0  X X^2+X X^2+X X^2+X  0 X^2  X X^2+X X^2+X X^2+X  X X^2 X^2+X  X X^2+X  0  0  X X^2+X X^2+X X^2  0 X^2  0 X^2+X  X X^2 X^2 X^2 X^2+X  0 X^2  0 X^2+X  X X^2  0  X  0  X  X X^2+X  0  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  0  X X^2+X  0  0 X^2+X  X X^2  X  0 X^2 X^2  0  X  X  0  X  0 X^2  0 X^2  X  0  X X^2+X  X X^2+X  X  0  X X^2+X  X  X X^2 X^2  X  0 X^2  0 X^2+X  X  X  0  X  0
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2+X  0  X X^2+X X^2 X^2  0 X^2+X  X  0  0  X X^2+X  0 X^2 X^2+X X^2  0  0  X  0  X  X  X X^2  X  0  X  X X^2+X X^2+X X^2  0 X^2 X^2  X X^2  X X^2+X X^2+X  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+64x^48+114x^49+164x^50+232x^51+267x^52+394x^53+457x^54+568x^55+717x^56+710x^57+848x^58+800x^59+693x^60+620x^61+389x^62+342x^63+224x^64+166x^65+148x^66+94x^67+68x^68+42x^69+38x^70+10x^71+14x^72+2x^73+3x^74+2x^75+1x^82

The gray image is a linear code over GF(2) with n=232, k=13 and d=96.
This code was found by Heurico 1.16 in 4.81 seconds.