The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2+X  1  1 X^2+X+2 X+2  X X^2+2  0
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  1  3 X^2+1 X+1 X+3 X^2+3 X^2+X+3  3 X^2+X+1  1 X+1 X^2+1 X^2+X+3 X^2+1 X^2+3 X+1 X+3  0  1  3  2  1  1  1  1  1
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  2  0  2  2  0  0  0  2  2  0  0  2  0  2  2  0  2  0  2  0  2  0  0  2  2  0  0  0  0
 0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  0  2  2  2  0  2  0  0  0  2  2  0  2  2  0  0  2  0  0  2  2  0  0  2  0  2  2  0  0  0  2  2  2  0  0
 0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  2  0  2  0  2  0  2  2  2  0  0  0  0  0  2  2  2  2  0  2  0  0  0  0  0  2  2  0  2  0  2  2  0  2  0  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+160x^56+144x^57+225x^58+240x^59+511x^60+240x^61+222x^62+144x^63+156x^64+1x^66+1x^68+1x^72+1x^84+1x^92

The gray image is a code over GF(2) with n=480, k=11 and d=224.
This code was found by Heurico 1.16 in 0.156 seconds.