The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+906x^54+2076x^55+4033x^56+5648x^57+7144x^58+8268x^59+9590x^60+8400x^61+7590x^62+5196x^63+3469x^64+1788x^65+884x^66+332x^67+110x^68+32x^69+52x^70+13x^72+4x^73

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 43.9 seconds.