The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+306x^57+415x^58+288x^59+138x^60+230x^61+343x^62+264x^63+12x^64+20x^65+16x^66+12x^67+2x^78+1x^84

The gray image is a code over GF(2) with n=480, k=11 and d=228.
This code was found by Heurico 1.16 in 0.156 seconds.