The generator matrix

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

generates a code of length 63 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+694x^60+616x^61+900x^62+416x^63+487x^64+312x^65+236x^66+80x^67+176x^68+48x^69+104x^70+25x^72+1x^80

The gray image is a code over GF(2) with n=504, k=12 and d=240.
This code was found by Heurico 1.16 in 140 seconds.