The generator matrix

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

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+50x^51+556x^52+1714x^53+3889x^54+7786x^55+13706x^56+20434x^57+28627x^58+34790x^59+37850x^60+35408x^61+30207x^62+21006x^63+12931x^64+6856x^65+3567x^66+1712x^67+662x^68+242x^69+70x^70+32x^71+22x^72+14x^73+6x^74+4x^77+2x^78

The gray image is a code over GF(2) with n=480, k=18 and d=204.
This code was found by Heurico 1.16 in 499 seconds.