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

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+55x^52+83x^54+231x^56+363x^58+178x^60+37x^62+20x^64+25x^66+26x^68+4x^70+1x^108

The gray image is a linear code over GF(2) with n=232, k=10 and d=104.
This code was found by Heurico 1.16 in 0.178 seconds.