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  2  0 2X+2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X+2  2  0 2X+2 2X+2 2X+2 2X  2  2  0 2X+2  0  0 2X 2X 2X  2  2  2  2  0 2X+2 2X 2X+2  0  0  0 2X  2 2X 2X+2  0 2X 2X 2X+2 2X
 0  0  2 2X+2  0  2 2X+2  0 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2 2X  0  2 2X+2  0  0  2 2X+2  0 2X+2 2X+2  0  2 2X  2 2X+2 2X+2 2X 2X+2  2  0  0 2X 2X  0  2  0  2 2X+2 2X 2X+2  0  2  2  0 2X+2 2X 2X  2  0 2X  0 2X+2 2X+2 2X+2 2X
 0  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  0 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0  0  0  0 2X  0  0  0  0 2X  0  0

generates a code of length 69 over Z4[X]/(X^2+2X+2) 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 0.313 seconds.