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  X  1  1  X  1  1  X  1  1  X  1  X  1  X  X  1  X  X X^2  1  X  X X^2  X  1  X  X  1 X^2  2 X^2  0  X  X X^2 X^2  X X^2  2  0  2  X X^2 X^2  2 X^2  1
 0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  2  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  0  2  2  0  2  2  0  0  2  0  2  2  2  0  2  0  2  0  2  0  0  2  2  0  0  0  2  0  0  0

generates a code of length 71 over Z4[X]/(X^3+2,2X) who�s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+1x^72+24x^73+2x^74+4x^75

The gray image is a code over GF(2) with n=568, k=5 and d=288.
This code was found by Heurico 1.16 in 0.203 seconds.