The generator matrix

 1  0  0  1  1  1  2  1  1  1  1  0  2 X^2  1  1 X^2+X+2  X  1  1  1 X^2+X+2  0  1  X X^2+X+2  1  1  1 X^2+X+2 X^2+2  1 X^2  1  1  1  1  1 X+2 X^2+2  1  X  1  1  1  0  1 X+2  1 X^2+X+2 X^2  1  1  X  1  X  0 X^2 X^2  1
 0  1  0  2 X^2+1 X^2+3  1 X^2 X^2+2  1  3  1  1  X X^2+X X^2+X+2  1  1 X+1 X+3  X  2 X^2 X+2  1  1  3 X^2+X+1 X^2+3 X^2+X  1 X^2+2  1  X X+1 X+2 X+1  2 X^2  1 X^2+X+3  1  1  2 X+2  X X+3  1 X^2  1  1 X^2+X X^2+X  X X^2+3 X^2+X+2  1  1  1  0
 0  0  1 X+3 X+1  2 X^2+X+1  X  3  1 X+2  X  3  1 X^2+X X^2+3 X^2+3  X X+1 X^2  0  1  1 X+3  0 X+1 X^2+X+2  1 X^2+2  1 X^2+3 X^2+3  2 X^2  X  3 X^2+X+3 X^2+X+1  1 X+1  2 X^2+X X^2 X+2 X^2+X+3  1 X^2+X+2 X^2 X^2+X+3  0 X^2+X+2 X^2+X+3  3  1 X^2+X+3  1 X^2+2 X+2 X^2+X+1  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+108x^56+538x^57+736x^58+660x^59+602x^60+456x^61+244x^62+296x^63+195x^64+106x^65+52x^66+52x^67+44x^68+4x^69+1x^72+1x^80

The gray image is a code over GF(2) with n=480, k=12 and d=224.
This code was found by Heurico 1.16 in 0.203 seconds.