The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+201x^56+532x^57+685x^58+552x^59+516x^60+476x^61+445x^62+272x^63+160x^64+104x^65+80x^66+48x^67+17x^68+4x^70+1x^74+1x^76+1x^78

The gray image is a code over GF(2) with n=480, k=12 and d=224.
This code was found by Heurico 1.16 in 0.344 seconds.