The generator matrix

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

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+442x^55+992x^56+1828x^57+1822x^58+2510x^59+1889x^60+2354x^61+1472x^62+1462x^63+693x^64+478x^65+238x^66+118x^67+49x^68+10x^69+8x^70+12x^71+2x^73+4x^74

The gray image is a code over GF(2) with n=480, k=14 and d=220.
This code was found by Heurico 1.16 in 2.64 seconds.