The generator matrix

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

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+552x^56+920x^57+1297x^58+1152x^59+1124x^60+884x^61+870x^62+452x^63+408x^64+228x^65+177x^66+76x^67+42x^68+8x^70+1x^72

The gray image is a code over GF(2) with n=480, k=13 and d=224.
This code was found by Heurico 1.16 in 3.41 seconds.