The generator matrix

 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  X  1  1  1  X  1  1  1  2  1  1  1 X^2+2  1  1  X  1  1  1  1  X  1  1 X^2 X^2  1  2  1 X^2+2  2  X  X  1
 0  X  0  X  0  2 X+2  X X^2 X^2+X X^2 X^2+X X^2 X^2+X+2 X^2+2 X^2+X X^2 X^2+X+2  2 X^2+X X+2  X X^2+X  0 X^2+2 X^2 X+2 X+2 X^2 X+2 X^2  2 X+2 X^2 X^2+2 X^2+X X^2+2  X X^2 X^2+2  X X^2 X^2+X  X  X X^2+X+2  2  X  X  X X^2+2  X  2  X  X  0 X+2 X^2+2
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2 X^2+X+2  X  0  2 X+2 X^2+X X^2+2  X  0 X^2+X X^2 X+2 X+2  X  0  2 X^2+X+2 X^2+X X^2+2  X X^2+X+2 X^2+X+2 X^2+2 X+2  X  0 X^2 X^2+X  2 X^2 X^2 X^2 X^2+X X+2  0  2  2 X^2+X X^2+X+2 X+2 X+2  X  X X^2+X  0  0 X^2+X  2 X^2+X
 0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  2  0  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  0  0  2  0  2  2  0  2  0  0  0  2  2  0  2  0  2  2  2  0  0  0  2  2  2  0
 0  0  0  0  2  2  0  0  2  2  2  2  0  2  0  2  2  0  2  0  0  0  0  0  2  2  2  2  0  0  0  0  2  0  2  2  2  0  0  0  2  2  2  0  2  2  0  2  0  2  0  2  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 53.

Homogenous weight enumerator: w(x)=1x^0+164x^53+212x^54+452x^55+363x^56+754x^57+463x^58+666x^59+288x^60+288x^61+135x^62+168x^63+51x^64+34x^65+21x^66+26x^67+8x^69+1x^70+1x^88

The gray image is a code over GF(2) with n=464, k=12 and d=212.
This code was found by Heurico 1.16 in 0.407 seconds.