The generator matrix

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

Homogenous weight enumerator: w(x)=1x^0+227x^54+188x^56+249x^58+162x^60+143x^62+31x^64+13x^66+6x^70+2x^74+2x^84

The gray image is a linear code over GF(2) with n=232, k=10 and d=108.
This code was found by Heurico 1.16 in 2.94 seconds.