The generator matrix

 1  0  1  1  1 X+2  1  X  1 2X  1  1 2X+2  1  1  1 3X+2  1  1  2  1 3X  1  1  1  1  1  1  0  1 3X+2  1 3X+2  1  1  X  1 2X+2 X+2  2  0  1  1  1  1  X  1  1  1  1  0  X  1  2  1  1  1  1  1  1
 0  1 X+1 3X+2  3  1  2  1 3X+3  1 3X  1  1 2X X+1 X+2  1 X+3 2X+2  1  X  1 X+1 X+3 2X+3 2X+1 2X+3  0  1 3X  1 3X+2  1 X+3  3 2X+2 2X+1  1  1  1  X  3 2X  1 3X+3  1 2X 3X 3X  2  1 2X+2 3X+3  X  1 2X+1 2X+3  3 2X+3  0
 0  0 2X+2  0  2 2X+2  0 2X+2  2  2  0 2X+2  2 2X+2 2X  2  0 2X 2X+2  0  2  0 2X 2X  0 2X 2X  0  0 2X 2X 2X+2  2  2 2X+2  2 2X  2  2  2 2X+2  0 2X+2 2X+2  2  0  0  2 2X  2 2X 2X 2X+2  0  0  0 2X 2X+2  2  0
 0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0  0 2X  0  0 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0
 0  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X  0 2X 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X  0 2X  0 2X 2X 2X  0 2X 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+60x^55+320x^56+376x^57+573x^58+396x^59+763x^60+490x^61+421x^62+234x^63+300x^64+86x^65+27x^66+12x^67+17x^68+2x^69+2x^71+4x^72+6x^73+2x^74+2x^76+1x^78+1x^80

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 0.375 seconds.