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

generates a code of length 73 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+14x^72+220x^73+14x^74+1x^80+4x^81+1x^82+1x^98

The gray image is a code over GF(2) with n=584, k=8 and d=288.
This code was found by Heurico 1.16 in 0.359 seconds.