The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2X+2) 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 0.187 seconds.