The generator matrix

 1  0  1  1  1 X^2+X+2  1  X  1  2  1  1 X^2  1  1  1 X^2+X  1  1 X^2+2  1 X+2  1  1  1  1  1  1  0  1 X+2  1  1  1  1  1  2  1  0 X^2+X  1  1 X^2+X+2  1 X^2  1 X^2+X  1  X  1  1  1  1 X^2  X  0  1  1
 0  1 X+1 X^2+X X^2+3  1 X^2+2  1 X^2+X+1  1 X+2  1  1  2 X+1 X^2+X+2  1 X^2+X+3 X^2  1  X  1 X+1 X^2+X+3 X^2+1  3 X^2+1  0  1 X+3  1 X^2+X+2 X^2+3 X^2  X X^2+X  1 X^2  1  1 X^2+X X^2+1  1  1  1 X+1  1  X X^2+X+2  0 X^2+X+2  0 X^2+X  0  X X^2 X^2  X
 0  0 X^2  0 X^2+2 X^2  0 X^2 X^2+2 X^2+2  0 X^2 X^2+2 X^2  2 X^2+2  0  2 X^2  0 X^2+2  0  2  2  0  2  2  0  0 X^2  0 X^2+2 X^2+2 X^2  0  2 X^2 X^2+2 X^2  2 X^2 X^2+2 X^2  0  2 X^2 X^2  2 X^2  0  2 X^2+2 X^2+2 X^2 X^2 X^2 X^2+2 X^2+2
 0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  2  2  0  2  2  0  0  2  0  0  2  2  2  0  0  0  2  0  2  2  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  2  0  0  0  2  2  2  2
 0  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  0  0  0  2  0  2  2  2  0  2  0  2  2  2  0  0  0  2  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  0  2  2  0  0  0  0  2  0

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+580x^54+944x^56+1184x^58+838x^60+436x^62+71x^64+24x^66+16x^70+2x^76

The gray image is a code over GF(2) with n=464, k=12 and d=216.
This code was found by Heurico 1.16 in 97.8 seconds.