The generator matrix

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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+93x^54+218x^55+568x^56+380x^57+608x^58+404x^59+740x^60+334x^61+378x^62+156x^63+157x^64+20x^65+5x^66+18x^67+3x^68+2x^69+2x^71+2x^72+3x^74+2x^75+1x^78+1x^84

The gray image is a code over GF(2) with n=472, k=12 and d=216.
This code was found by Heurico 1.16 in 0.36 seconds.