The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+622x^56+808x^57+1394x^58+960x^59+1245x^60+872x^61+892x^62+504x^63+444x^64+144x^65+202x^66+40x^67+49x^68+8x^70+5x^72+2x^76

The gray image is a code over GF(2) with n=480, k=13 and d=224.
This code was found by Heurico 1.16 in 0.906 seconds.