The generator matrix

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

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+70x^56+304x^57+209x^58+334x^59+232x^60+364x^61+184x^62+256x^63+49x^64+20x^65+19x^66+2x^67+3x^74+1x^98

The gray image is a code over GF(2) with n=480, k=11 and d=224.
This code was found by Heurico 1.16 in 0.219 seconds.