The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1  2 2X+2 2X+2  1  1  1 X+2  X  1  1 3X  2  1 3X  1  1  1 3X+2  X 2X+2  1 2X  1 X+2 3X+2  X  0  1  1  X  1  1 X+2  1  1  1  1  X 2X+2  2  1  1  1 3X 2X X+2 X+2 3X+2  1
 0  1  0 2X  3 2X+3  1  X X+3 3X 3X+3  1  X  1 2X+2 2X+1 3X+1  1  0 3X  1  1  1  X X+2  2 2X+3 X+3  1  1 2X+2 2X+2  1 3X+1  1  1  X  1 3X+2 3X+1  1 2X+3 X+2  1 3X+2 3X+2 2X+2  0  1  1  1 2X 3X  0  1  1  X  1  1  0
 0  0  1 3X+1 X+1 2X X+1  X 2X+1  1 3X 3X  1 X+1 X+2 2X+3  2 X+2  1 3X+1 3X+2 X+1  1 2X+2  1  3 3X 3X+3 2X+3 2X  1 X+3 2X+3 X+1 2X+2  1  1 2X+2 3X+1 2X+1 3X+3  2 2X 3X+3 2X+3  X 2X+2  X 3X  2 X+2 2X+1  0 X+3 3X+2 X+2  1 2X 2X+2  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+104x^56+538x^57+814x^58+522x^59+664x^60+338x^61+460x^62+244x^63+141x^64+116x^65+52x^66+54x^67+33x^68+12x^69+1x^70+1x^72+1x^82

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 0.188 seconds.