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 X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X^2 X+2  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2  X  0 X^2+X+2  2 X^2+X+2 X^2+2 X^2+X X^2  X  X  2 X^2 X^2+X+2 X+2  X  0  0
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  0  0  0  2  2  0  2  2  2  2  0  0  0  2  2  0  0  0  0  2  2  2  2  2  0  2  0  0  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  2  2  0  2  0  0  2  2  0  0  2  0  2  0  2  2  0  2  0  0  0  2  2  2  2  2  0  0  0
 0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  2  2  0  2  0  0  0  2  2  0  2  0  0  2  2  0  0  0  2  0  0  2  2  0  2  0  0

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+23x^56+48x^58+64x^59+752x^60+64x^61+48x^62+23x^64+1x^120

The gray image is a code over GF(2) with n=480, k=10 and d=224.
This code was found by Heurico 1.16 in 0.203 seconds.