The generator matrix

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

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+60x^55+320x^56+376x^57+573x^58+396x^59+763x^60+490x^61+421x^62+234x^63+300x^64+86x^65+27x^66+12x^67+17x^68+2x^69+2x^71+4x^72+6x^73+2x^74+2x^76+1x^78+1x^80

The gray image is a code over GF(2) with n=480, k=12 and d=220.
This code was found by Heurico 1.16 in 0.375 seconds.