The generator matrix

 1  0  0  1  1  1  2  2 2X+2  1  1  2  1  1 3X  1  1 3X  X  1  1  1 X+2 3X+2  1  1 3X+2 2X 2X X+2  1  1  1  1  1  1 2X  X 3X  1  2  1  1  1 2X+2  1  1  1  1 3X+2  X  1  1  1  1 X+2 2X  0  1  2
 0  1  0  0  3  3  1  X  1 2X 2X+3  1  2  1 3X+2 3X 3X+3  1  1 3X+3 3X+2 3X+1  1 2X+2 X+1 X+2  1  1  1  X  1 2X X+3 X+3 2X+1 3X+1 3X  1  1  X  1 2X  1 3X  1 2X+3 3X+1 2X+1 3X+2 2X+2  1 2X 2X+1  X 2X+1  1  1  1 3X+3 3X
 0  0  1 X+1 3X+1 2X 3X+3  1 3X  X 3X  3  3 2X+3  1  1  2  3 3X 2X+1  X 3X+1  0  1  2 X+1 3X+3  2 3X+1  1  0  3 X+1 2X+3 X+3 3X  1  0 2X+1 3X 2X+1  X 2X+2 3X+1 2X 2X+1 3X+3 3X+1  3  1 X+3 X+3 3X+1  2 X+2 2X+1 X+3 3X+2 3X+1  1
 0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0  0  0  0  0  0 2X  0  0  0 2X  0  0 2X  0  0 2X  0 2X  0 2X  0 2X 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+641x^56+648x^57+1554x^58+928x^59+1480x^60+656x^61+916x^62+416x^63+457x^64+104x^65+282x^66+64x^67+42x^68+1x^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 54.9 seconds.