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

generates a code of length 66 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+768x^62+254x^64+2048x^66+256x^68+768x^70+1x^128

The gray image is a code over GF(2) with n=528, k=12 and d=248.
This code was found by Heurico 1.16 in 0.547 seconds.