The generator matrix

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

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+321x^54+1016x^55+2175x^56+2800x^57+3538x^58+4244x^59+4830x^60+4210x^61+3912x^62+2472x^63+1575x^64+948x^65+414x^66+148x^67+90x^68+26x^69+31x^70+8x^71+1x^72+8x^74

The gray image is a code over GF(2) with n=480, k=15 and d=216.
This code was found by Heurico 1.16 in 8.8 seconds.