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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1
 0  X  0  X  0  0 X^2+X X^2+X  0  0  X X^2+X  0  0 X^2+X  X  0 X^2  X X^2+X X^2 X^2 X^2+X X^2+X  0  X  X X^2  0 X^2 X^2+X  X X^2 X^2+X  X  X X^2  0 X^2+X X^2 X^2+X X^2 X^2+X  0 X^2  0 X^2+X  0  X X^2 X^2 X^2  X  X  X  X  0  0
 0  0  X  X  0 X^2+X X^2+X  0  0 X^2+X  X  0  0  X X^2+X  0 X^2  X  X X^2  0  X X^2+X  0 X^2 X^2+X X^2  X X^2  X  0  X X^2  X  0 X^2+X X^2+X  X X^2 X^2  X X^2+X X^2 X^2  0 X^2+X X^2+X X^2+X X^2+X  0 X^2+X X^2 X^2 X^2 X^2+X  0  0  0
 0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 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+17x^54+24x^55+28x^56+40x^57+291x^58+40x^59+32x^60+24x^61+11x^62+3x^64+1x^114

The gray image is a linear code over GF(2) with n=232, k=9 and d=108.
This code was found by Heurico 1.16 in 0.116 seconds.