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

generates a code of length 60 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+212x^55+142x^56+568x^57+210x^58+786x^59+376x^60+896x^61+148x^62+342x^63+101x^64+152x^65+26x^66+94x^67+18x^68+16x^69+6x^71+1x^76+1x^92

The gray image is a code over GF(2) with n=480, k=12 and d=220.
This code was found by Heurico 1.16 in 0.516 seconds.