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

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

Homogenous weight enumerator: w(x)=1x^0+178x^55+185x^56+444x^57+345x^58+726x^59+545x^60+704x^61+279x^62+290x^63+121x^64+108x^65+31x^66+82x^67+27x^68+24x^69+1x^70+4x^71+1x^96

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 0.437 seconds.