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  X  X  X  X  X  X  1  1  1  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2
 0 2X+2  0  2  0  0  2 2X+2 2X 2X 2X+2  2 2X 2X 2X+2  2  0 2X  2 2X+2  0 2X  2 2X+2 2X  0 2X+2  2 2X 2X  2 2X+2  0  2  2  0 2X+2  2 2X+2 2X+2 2X  0 2X+2  2  0  0 2X 2X  0 2X  2 2X+2  0 2X  2 2X+2 2X  0 2X+2  2 2X  0 2X+2  2  0 2X  2 2X+2  0  0 2X+2 2X+2 2X
 0  0 2X+2  2 2X  2 2X+2 2X 2X  2 2X+2 2X  0 2X+2  2  0  0  2  2  0 2X 2X+2 2X+2 2X 2X 2X+2 2X+2 2X  0  2  2  0 2X+2 2X 2X+2  2  2  0 2X+2  2 2X+2  2 2X  0  0 2X 2X  0  0  2  2  0 2X 2X+2 2X+2 2X 2X 2X+2 2X+2 2X  0  2  2  0  0  2  2  0 2X 2X+2 2X+2 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+76x^72+128x^73+32x^74+16x^76+2x^88+1x^112

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 0.265 seconds.