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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+65x^66+160x^67+10x^68+10x^70+5x^72+1x^74+4x^82

The gray image is a code over GF(2) with n=536, k=8 and d=264.
This code was found by Heurico 1.16 in 1.12 seconds.