The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+14x^69+101x^70+274x^71+247x^72+274x^73+90x^74+14x^75+7x^76+1x^78+1x^132

The gray image is a code over GF(2) with n=576, k=10 and d=276.
This code was found by Heurico 1.16 in 0.234 seconds.