The generator matrix

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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+90x^52+314x^53+385x^54+450x^55+381x^56+422x^57+367x^58+350x^59+269x^60+324x^61+202x^62+174x^63+138x^64+94x^65+75x^66+26x^67+9x^68+14x^69+3x^70+8x^71

The gray image is a linear code over GF(2) with n=232, k=12 and d=104.
This code was found by Heurico 1.11 in 0.25 seconds.