The generator matrix

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

generates a code of length 60 over Z4[X]/(X^3+2,2X) 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 0.109 seconds.