The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+404x^55+1039x^56+1930x^57+1707x^58+2380x^59+2206x^60+2146x^61+1470x^62+1404x^63+709x^64+552x^65+247x^66+116x^67+43x^68+26x^69+1x^72+2x^73+1x^76

The gray image is a code over GF(2) with n=480, k=14 and d=220.
This code was found by Heurico 1.16 in 2.5 seconds.