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

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

Homogenous weight enumerator: w(x)=1x^0+100x^66+124x^67+101x^68+120x^69+22x^70+4x^71+24x^72+6x^73+5x^74+1x^76+1x^80+2x^81+1x^82

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 0.281 seconds.