The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+460x^53+1767x^54+4632x^55+7024x^56+10688x^57+13565x^58+18230x^59+18469x^60+17774x^61+14600x^62+10970x^63+6239x^64+4028x^65+1505x^66+706x^67+256x^68+82x^69+51x^70+6x^71+10x^72+8x^73+1x^84

The gray image is a code over GF(2) with n=480, k=17 and d=212.
This code was found by Heurico 1.16 in 129 seconds.