The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  X X^2+2  1  1  1  1  X  0  1  X X^2+2  X  1  1  X  1  X  X  2 X^2  1  1  1  X  X  2 X^2  X  X  X  X  X  X  1  1  1  1  1  1  X  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X X^2+X  X  0 X+2  X X^2+X X^2+2 X+2  0 X^2+X  X X^2+2 X+2  X X^2+2 X^2+X+2 X+2  0  2 X^2+X+2  X  X  X  2 X^2 X^2 X^2+X+2  X  X  X  2 X^2+2  0 X^2 X^2  2 X^2+X  X X^2+X+2  X  0 X^2+2 X^2+2  0
 0  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  0  2  0  0  2  2  2  2  0  0  0  2  2  2  0  2  2  2  0  2  0  0  2  0  0  2  0  2  2  0  0  0  2  0  2  0  0  2  0  2  0  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+12x^58+32x^59+164x^60+28x^61+10x^62+3x^64+4x^69+2x^70

The gray image is a code over GF(2) with n=480, k=8 and d=232.
This code was found by Heurico 1.16 in 0.172 seconds.