The generator matrix

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

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+962x^54+2044x^55+4011x^56+4956x^57+8300x^58+8220x^59+9189x^60+8148x^61+7896x^62+4928x^63+3788x^64+1552x^65+992x^66+324x^67+163x^68+28x^69+24x^70+4x^71+4x^73+2x^78

The gray image is a code over GF(2) with n=480, k=16 and d=216.
This code was found by Heurico 1.16 in 81.7 seconds.