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

generates a code of length 73 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+30x^70+102x^71+259x^72+248x^73+251x^74+96x^75+28x^76+6x^78+2x^79+1x^130

The gray image is a code over GF(2) with n=584, k=10 and d=280.
This code was found by Heurico 1.16 in 0.25 seconds.