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 2X  X 2X+2  X  0  X  X  2  X  X  X  0  X  X  2  X  X  0  2  X  X 2X+2 2X  X  X  1  1
 0  X  0 X+2  0 3X+2  0 3X 2X+2 3X+2  2  X 2X+2 X+2  2 3X 2X 3X+2 2X  X 2X X+2 2X 3X  2 X+2 2X+2 3X  2 3X+2 2X+2  X 3X+2  X 3X  X X+2  X 2X+2  X  X  2 2X X+2  X X+2 3X  X  0  X  X  X  0  2  2  0 2X 2X+2 2X  2
 0  0  2 2X+2 2X  2 2X+2 2X 2X+2  0  0 2X+2  2 2X 2X  2 2X 2X 2X+2  2  0  0  2 2X+2  2  2 2X  0 2X+2 2X+2  0 2X  0 2X+2 2X  2 2X+2  0  2 2X+2 2X  2 2X+2  0 2X+2  2  2  2 2X+2 2X 2X  0  0  0 2X 2X 2X 2X 2X+2  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+118x^58+168x^59+60x^60+20x^61+66x^62+64x^63+1x^64+4x^65+4x^66+2x^68+4x^74

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 0.219 seconds.