The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  X  2  1  1  1  1  X  0  1  X  2  X  1  1  X  1  X  X 2X 2X+2  1  1  1  X  X 2X 2X+2  X  X  X  X  X  X  1  1  1  1  1  1  X  1
 0  X  2 3X+2  0 3X+2  2 3X 2X X+2 2X+2 3X 2X X+2 2X+2  X 3X+2  X  0 3X  X 3X+2  2 3X  0 3X+2  X  2 3X  X  2 X+2 3X  0 2X X+2  X  X  X 2X 2X+2 2X+2 X+2  X  X  X 2X  2  0 2X+2 2X+2 2X 3X+2  X X+2  X  0  2  2  0
 0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0  0 2X  0  0 2X  0 2X 2X  0  0  0 2X  0 2X  0  0 2X  0 2X  0  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+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 0.187 seconds.