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

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

Homogenous weight enumerator: w(x)=1x^0+44x^58+64x^59+806x^60+64x^61+44x^62+1x^120

The gray image is a code over GF(2) with n=480, k=10 and d=232.
This code was found by Heurico 1.16 in 0.25 seconds.