The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+406x^56+320x^57+580x^58+448x^59+622x^60+448x^61+568x^62+320x^63+360x^64+4x^66+2x^68+15x^72+1x^80+1x^88

The gray image is a code over GF(2) with n=480, k=12 and d=224.
This code was found by Heurico 1.16 in 24.2 seconds.