The generator matrix

 1  0  1  1  1 X^2+X  1  1 X+2  1  1 X^2+2  1  1 X^2+2  1  1 X+2  1  1 X^2+X  1  1  0  1  1  2  1  1 X^2+X+2  1  1  1  1 X^2  X  1  1  1  1  1  1  1  1  2 X^2+X+2 X^2  X  X  X  0  X  X X^2+2  X  X  0  X  X X^2+2  X  X  X  X  1 X^2+2  2  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  2 X+3  1 X^2+X+2 X^2+3  1 X^2  X X^2+X+1  1  1  1  2 X^2+X+2 X^2  X X+3 X^2+3 X^2+X+1  1  1  1  1  1  0 X^2+X  X X^2+2 X+2  X  0 X^2+X  X X^2+2 X+2  X  2 X^2 X^2  2 X^2+X+3  1  0  0
 0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  0  2  2  0  2  0  2  0  2  2  2  2  0  0  0  0  2  0  2  0  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  2  2  2  2  0  0  0  0  0  0  2  0  2  0  0  0  2  0

generates a code of length 68 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+39x^66+232x^67+67x^68+72x^69+45x^70+32x^71+16x^72+4x^74+4x^76

The gray image is a code over GF(2) with n=544, k=9 and d=264.
This code was found by Heurico 1.16 in 0.172 seconds.