The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+580x^53+1865x^54+4226x^55+7182x^56+10028x^57+15287x^58+16826x^59+19164x^60+16570x^61+15755x^62+10620x^63+6593x^64+3616x^65+1704x^66+670x^67+248x^68+86x^69+24x^70+6x^71+12x^72+4x^74+4x^75+1x^82

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 137 seconds.