The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+351x^52+1572x^53+3740x^54+7836x^55+13353x^56+20616x^57+27948x^58+36364x^59+38035x^60+36528x^61+28794x^62+21360x^63+12700x^64+7256x^65+3464x^66+1404x^67+522x^68+172x^69+80x^70+12x^71+28x^72+4x^74+2x^78+2x^80

The gray image is a code over GF(2) with n=480, k=18 and d=208.
This code was found by Heurico 1.16 in 502 seconds.