The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+313x^54+972x^55+1948x^56+3270x^57+3398x^58+4492x^59+4434x^60+4466x^61+3483x^62+2846x^63+1480x^64+850x^65+456x^66+208x^67+68x^68+38x^69+30x^70+10x^71+5x^72

The gray image is a code over GF(2) with n=480, k=15 and d=216.
This code was found by Heurico 1.16 in 9.7 seconds.