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

generates a code of length 72 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+56x^70+394x^72+56x^74+3x^76+1x^96+1x^108

The gray image is a code over GF(2) with n=576, k=9 and d=280.
This code was found by Heurico 1.16 in 0.344 seconds.