The generator matrix

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

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+428x^62+312x^63+702x^64+344x^65+670x^66+328x^67+628x^68+264x^69+280x^70+32x^71+74x^72+18x^74+8x^78+1x^80+4x^82+2x^88

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 77.8 seconds.