The generator matrix

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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+184x^55+308x^56+200x^57+64x^58+44x^60+72x^63+91x^64+56x^65+4x^68

The gray image is a linear code over GF(2) with n=232, k=10 and d=110.
This code was found by Heurico 1.16 in 56.3 seconds.