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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+104x^67+129x^68+96x^69+108x^70+20x^71+12x^72+30x^73+2x^74+4x^75+1x^76+1x^78+1x^80+2x^81+1x^86

The gray image is a code over GF(2) with n=552, k=9 and d=268.
This code was found by Heurico 1.16 in 0.531 seconds.