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^2 X^2  1  X  1  X  X  X  1  X  X  X  X  X  X  X  X  X  X  1  X  X
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  2  2  0  2  2  0  0
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  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  0  0  2  2  0  2  2  0  0  2  2  0  0  0  2  2  0  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  0  0  2  2  2  2  0  0  0  0  0  0  2  0  2  2
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  2  0  0  2  0  0  0  0  2  2  2  0  2  2  2  2  0  0  0  0  2  2
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  2  2  0  0  2  0  2  0  2  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+29x^66+32x^67+41x^68+320x^69+27x^70+32x^71+19x^72+5x^74+3x^76+1x^78+2x^98

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 137 seconds.