The generator matrix

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

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+870x^54+2136x^55+3932x^56+5600x^57+7516x^58+8324x^59+9232x^60+8336x^61+7566x^62+5096x^63+3781x^64+1872x^65+720x^66+324x^67+140x^68+32x^69+32x^70+24x^71+2x^72

The gray image is a code over GF(2) with n=480, k=16 and d=216.
This code was found by Heurico 1.16 in 102 seconds.