The generator matrix

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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+120x^51+339x^52+528x^53+592x^54+738x^55+820x^56+788x^57+792x^58+698x^59+662x^60+558x^61+478x^62+400x^63+261x^64+160x^65+116x^66+90x^67+27x^68+14x^69+6x^70+2x^71+2x^72

The gray image is a linear code over GF(2) with n=232, k=13 and d=102.
This code was found by Heurico 1.16 in 2.31 seconds.