The generator matrix

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

generates a code of length 58 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+33x^52+96x^53+270x^54+292x^55+556x^56+456x^57+715x^58+444x^59+576x^60+272x^61+225x^62+92x^63+47x^64+8x^65+2x^66+4x^67+3x^68+1x^70+2x^74+1x^82

The gray image is a code over GF(2) with n=464, k=12 and d=208.
This code was found by Heurico 1.16 in 0.281 seconds.