The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X X^2+X  1  1  X  1  1  1  1 X^2+X  X  1  1  1  1  X X^2+X X^2+X  X  0  1  X  0 X^2+X  0  0  1  1  1 X^2 X^2+X  1  1 X^2  0  1 X^2+X  1  X  1 X^2 X^2  0  0  0  1  1
 0  1  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2+X  X  X X^2+1 X^2+X+1  1 X^2+1  1  1 X^2+X+1 X+1 X^2+X+1 X+1  1  1  1  1 X^2+X X^2+1  1  1  1 X^2+X  1  0  X X+1  1 X^2 X^2+X+1  X  X X^2 X^2+X  1 X^2+X X^2 X^2+1  1  1  1 X^2  0 X^2  0
 0  0  1  0  0  0 X^2+1  1  1 X^2+1  0  1  1 X+1 X^2+X X^2+X X^2  0 X^2+X X^2+1 X^2  0 X^2+X+1  1 X+1 X^2+X X^2+X  1  1 X^2+X+1 X^2  X X^2+X  1 X^2+X+1  0  X X^2+X+1 X+1 X+1 X+1  1 X^2+1  X  1  1 X^2+X+1 X^2+X+1 X^2  0 X^2  0  X  0  1 X^2 X^2  0
 0  0  0  1  0  1  1  0 X^2+1 X^2+1  X X^2+X+1  0  X  1  1 X^2 X+1  1 X+1 X^2+1 X^2+1 X^2+1 X^2+X  X X^2  0  1  X  X  1  0 X^2+X+1 X+1 X^2  1 X^2+X  0 X^2+X+1 X^2 X^2+X+1  1  1  X  1 X^2+X X+1 X^2  X X^2+X X^2+1  0 X^2+X+1  0 X^2  1  0 X^2
 0  0  0  0  1  1 X^2 X^2+1  1 X+1 X^2+X+1 X^2 X+1  X X^2+X X^2+X+1 X+1 X^2 X^2+1 X^2+1 X+1  X  0 X^2  1 X^2 X^2+X+1  0  1 X^2 X+1  0  X  1  X X^2+X  X X+1 X^2+X  0  0 X^2+X+1 X^2+1 X^2  X X^2+X X^2+X+1 X^2+1 X+1  1 X^2+X  X X^2+X+1  1  0  X X^2+X X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 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+104x^48+374x^49+966x^50+1630x^51+2227x^52+2774x^53+4288x^54+4456x^55+6269x^56+5906x^57+7033x^58+6158x^59+6455x^60+4952x^61+4317x^62+2838x^63+2138x^64+1146x^65+753x^66+372x^67+198x^68+74x^69+47x^70+34x^71+12x^72+6x^73+4x^74+4x^76

The gray image is a linear code over GF(2) with n=232, k=16 and d=96.
This code was found by Heurico 1.13 in 44.6 seconds.