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  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2 X^2 X^2+2  0 X^2 X^2 X^2  2 X^2+2 X^2+2  0 X^2  0  0  2  2  2 X^2+2 X^2+2 X^2+2 X^2+2  0 X^2  2 X^2  0  0  0  2 X^2+2  2 X^2  0  2  2 X^2  2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  0 X^2+2 X^2  0  0 X^2+2 X^2  0 X^2 X^2  0 X^2+2  2 X^2+2 X^2 X^2  2 X^2 X^2+2  0  0  2  2  0 X^2+2  0 X^2+2 X^2  2 X^2  0 X^2+2 X^2+2  0 X^2  2  2 X^2+2  0  2  0 X^2 X^2 X^2  2
 0  0  0  2  2  2  0  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  0  2  2  2  2  2  0  0  0  2  2  2  0  2  0  0  0  0  2  0  0  0  0  2  0  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+7x^66+12x^67+56x^68+360x^69+54x^70+12x^71+7x^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 0.297 seconds.