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  X  1  0  1  1  1  0  X  1  1  0  X  1  0  1 X^2  1  1  1  1  1
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X X^2+X X^2+X X^2 X^2  0  X X^2  X  X X^2  0  X X^2+X  X  0  0  0  X  0 X^2+X  0 X^2 X^2  0  X  X  0  X X^2  X X^2+X X^2 X^2+X X^2+X X^2  X  0  X  X  0  0  X  X X^2+X X^2+X  0
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0 X^2  X X^2 X^2+X  0 X^2+X X^2+X X^2 X^2 X^2+X  0 X^2+X  0  0  0  X X^2  X  X  X  0  X X^2 X^2+X  X X^2+X X^2+X  0  0 X^2 X^2+X  X X^2  0 X^2 X^2 X^2 X^2+X  0 X^2+X X^2 X^2 X^2 X^2+X X^2  0
 0  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  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+58x^52+8x^53+88x^54+40x^55+200x^56+80x^57+170x^58+80x^59+111x^60+40x^61+56x^62+8x^63+34x^64+28x^66+10x^68+8x^70+1x^72+2x^74+1x^100

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 0.168 seconds.