The generator matrix

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

generates a code of length 66 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+256x^63+254x^64+512x^65+256x^66+512x^67+256x^71+1x^128

The gray image is a code over GF(2) with n=528, k=11 and d=252.
This code was found by Heurico 1.16 in 0.343 seconds.