The generator matrix

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

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+166x^55+209x^56+450x^57+501x^58+520x^59+604x^60+570x^61+382x^62+226x^63+142x^64+158x^65+53x^66+60x^67+27x^68+22x^69+4x^71+1x^92

The gray image is a code over GF(2) with n=480, k=12 and d=220.
This code was found by Heurico 1.16 in 0.578 seconds.