The generator matrix

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

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+108x^58+250x^59+337x^60+220x^61+83x^62+10x^63+14x^64+1x^114

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 14.4 seconds.