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  2  1  X  1  1  X  1  1  1  X  X  X  1  0  1  X X^2 X^2  0
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  0 X^2+2 X^2 X^2 X^2 X^2+2 X^2  2  0 X^2 X^2  0  2 X^2+2 X^2+2 X^2 X^2  0  0  2  0  2  0 X^2+2  0 X^2  2 X^2 X^2+2  2  2  0  0 X^2 X^2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  0 X^2+2 X^2  0  0 X^2+2 X^2  0 X^2 X^2+2  0  2 X^2 X^2+2  0  2 X^2 X^2+2 X^2 X^2+2  0  2 X^2+2 X^2+2 X^2+2 X^2+2  0  2  2  2 X^2+2 X^2+2  0  2  0  2  0  0 X^2 X^2 X^2 X^2+2  0  0
 0  0  0  2  2  2  0  2  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  2  2  2  2  0  0  2  2  0  2  2  0  0  2  0  2  2  0  0  0  2  0  0  2  2  0  2  2  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+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 60.2 seconds.