The generator matrix

 1  0  0  0  1  1  1  0  0 X^2  1  1  1  1 X^2+X X^2  1 X^2+X X^2  1  1 X^2  1  1  1  X  1 X^2+X X^2+X  1 X^2  1 X^2  1  X  1  1 X^2  X  1  X  1 X^2+X X^2+X  1  X X^2  1 X^2  0 X^2+X  0  1  1 X^2 X^2+X  1  1
 0  1  0  0  0 X^2 X^2 X^2  1  1 X+1  1  1 X^2+1  1  1  X X^2+X  0 X^2+X X+1  X X^2 X+1 X^2+X  1 X+1  1  1  X  1 X^2+X+1  1  1  1  1  X  1  1 X+1 X^2 X^2+1  1  1 X^2+1 X^2+X  1 X^2+X+1 X^2  X  0  1 X^2+X+1 X^2  1  1 X^2 X^2
 0  0  1  0 X^2  1 X^2+1  1 X+1  0  1 X^2+X X^2 X+1 X+1  X  0  1  1 X+1 X^2+X X^2  X  0  1 X^2+X+1 X^2+X+1 X^2+X  1  X X^2+X+1 X+1 X+1 X^2+1  0  X X^2+1  1  X X^2+X+1  0 X^2  X X^2  0  0 X^2+1  X  1  X X^2+X  X  1  X X+1 X^2+X X^2+X+1  0
 0  0  0  1 X^2+X+1 X^2+X+1  0 X+1 X^2  1  1  1 X^2  0 X^2+X+1 X^2 X^2  1  X X^2+X X+1  1  1  X X^2+1  X  0 X^2  X X+1 X^2+1  1 X+1 X+1 X+1 X^2+X  X X+1 X^2+1  X  1  X  X  0 X^2+X+1  1 X^2+1 X^2+1 X^2+1  1  1  X X+1 X^2  X X^2+X X^2+X+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+92x^52+292x^53+413x^54+422x^55+414x^56+426x^57+357x^58+306x^59+333x^60+292x^61+234x^62+168x^63+103x^64+98x^65+77x^66+26x^67+17x^68+12x^69+7x^70+6x^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 1.16 in 0.577 seconds.