The generator matrix

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

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+264x^62+96x^63+301x^64+96x^65+264x^66+2x^96

The gray image is a code over GF(2) with n=512, k=10 and d=248.
This code was found by Heurico 1.16 in 0.14 seconds.