The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+564x^55+840x^56+1878x^57+1979x^58+2242x^59+1776x^60+2318x^61+1693x^62+1548x^63+684x^64+540x^65+163x^66+68x^67+26x^68+46x^69+4x^70+8x^71+1x^72+2x^73+2x^75+1x^78

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 74.1 seconds.