The generator matrix

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

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+86x^55+77x^56+100x^57+52x^58+56x^59+45x^60+56x^61+10x^62+18x^63+4x^64+1x^66+4x^69+1x^76+1x^90

The gray image is a linear code over GF(2) with n=232, k=9 and d=110.
This code was found by Heurico 1.16 in 0.111 seconds.