The generator matrix

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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+302x^55+454x^56+554x^57+553x^58+536x^59+543x^60+516x^61+251x^62+194x^63+97x^64+46x^65+10x^66+24x^67+8x^68+4x^69+1x^70+1x^76+1x^82

The gray image is a code over GF(2) with n=472, k=12 and d=220.
This code was found by Heurico 1.16 in 1.55 seconds.