The generator matrix

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

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+454x^60+128x^61+472x^62+508x^64+128x^65+232x^66+120x^68+3x^80+2x^84

The gray image is a code over GF(2) with n=504, k=11 and d=240.
This code was found by Heurico 1.16 in 1.83 seconds.