The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  2  X  X  X  2  1  1
 0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X+2 2X+2 2X+2  2 2X+2 2X+2 2X+2  2  0  0  0 2X  0  0  0 2X 2X 2X 2X+2  2  2 2X+2  2  2 2X+2 2X+2  0  0
 0  0 2X  0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0  0  0  0
 0  0  0  0 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X  0  0  0  0  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+12x^56+108x^58+284x^60+80x^62+19x^64+2x^66+4x^68+2x^82

The gray image is a code over GF(2) with n=480, k=9 and d=224.
This code was found by Heurico 1.16 in 0.172 seconds.