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

generates a code of length 58 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+164x^54+406x^56+256x^57+540x^58+256x^59+239x^60+92x^62+57x^64+36x^66+1x^108

The gray image is a code over GF(2) with n=464, k=11 and d=216.
This code was found by Heurico 1.16 in 28.5 seconds.