The generator matrix

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

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+406x^56+320x^57+580x^58+448x^59+622x^60+448x^61+568x^62+320x^63+360x^64+4x^66+2x^68+15x^72+1x^80+1x^88

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 24.5 seconds.