The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+764x^57+412x^58+1048x^59+320x^60+632x^61+192x^62+328x^63+59x^64+212x^65+36x^66+64x^67+24x^69+4x^72

The gray image is a code over GF(2) with n=480, k=12 and d=228.
This code was found by Heurico 1.16 in 103 seconds.