The generator matrix

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

generates a code of length 66 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+501x^60+1178x^61+2221x^62+2542x^63+3826x^64+3994x^65+4760x^66+3878x^67+3811x^68+2336x^69+1852x^70+898x^71+567x^72+202x^73+60x^74+58x^75+44x^76+18x^77+19x^78+2x^80

The gray image is a code over GF(2) with n=528, k=15 and d=240.
This code was found by Heurico 1.16 in 10.1 seconds.