The generator matrix

 1  0  0  1  1  1  0  X  1 X^2  1  1  X  1 X^2+X  X  X  0  1  0  1  1  1  1  1  1  1  0 X^2  X  X  0 X^2  X X^2 X^2+X X^2+X  X  1  1  1  1 X^2  1  1  1  X  1  X  1 X^2+X  0  1  1  1  1  1  0
 0  1  0  0  1  1  1 X^2 X^2+1  1 X^2 X+1  1  X  1 X^2+X  1 X^2+X  X  1 X^2+X X^2+X+1 X+1 X^2+X X^2+X+1 X^2 X^2+1  1  1  1  1  1  1  1  1  1  1  1  0  0  1  1  1 X+1 X^2+X+1  0  1  X  X X^2+X X^2  1  X  0  0 X^2+1 X+1  1
 0  0  1  1 X^2 X^2+1  1  1  X X^2+X X^2+X X^2+1 X^2+X+1  1 X^2+1  1  0  1  1 X^2+X+1  X X^2+X X^2+1 X^2  0  1 X^2+1  X X^2+X X^2  X  0  1 X^2+X+1 X+1  1 X^2+X  0 X+1 X^2+X+1 X+1 X^2+X+1 X^2 X+1 X^2+X+1  X X^2+X X+1  1 X^2+X+1  1  1 X^2+X X^2 X^2+X  0  X  1
 0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  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 54.

Homogenous weight enumerator: w(x)=1x^0+184x^54+280x^56+240x^58+126x^60+106x^62+38x^64+36x^66+1x^68+10x^70+1x^72+1x^76

The gray image is a linear code over GF(2) with n=232, k=10 and d=108.
This code was found by Heurico 1.11 in 0.079 seconds.