The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+20x^58+252x^59+20x^60+170x^61+8x^62+24x^63+8x^64+2x^65+3x^66+3x^68+1x^70

The gray image is a code over GF(2) with n=480, k=9 and d=232.
This code was found by Heurico 1.16 in 0.125 seconds.