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 2X 2X  1  X  1  1  X  1  1  1  X  X  X  1  0  1  X 2X+2 2X+2  0
 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  0  2 2X+2 2X+2 2X+2  2 2X+2 2X  0 2X+2 2X+2  0 2X  2  2 2X+2 2X+2  0  0 2X  0 2X  0  2  0 2X+2 2X 2X+2  2 2X 2X  0  0 2X+2 2X+2
 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  2  0 2X 2X+2  2  0 2X 2X+2  2 2X+2  2  0 2X  2  2  2  2  0 2X 2X 2X  2  2  0 2X  0 2X  0  0 2X+2 2X+2 2X+2  2  0  0
 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  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X  0  0 2X 2X  0 2X 2X 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+212x^66+136x^68+126x^70+18x^72+8x^74+2x^76+6x^78+1x^80+2x^84

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 59.6 seconds.