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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+9x^66+86x^68+320x^69+84x^70+9x^72+1x^74+2x^102

The gray image is a code over GF(2) with n=552, k=9 and d=264.
This code was found by Heurico 1.16 in 0.313 seconds.