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

generates a code of length 72 over Z4[X]/(X^3+2,2X) who�s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+52x^70+96x^71+219x^72+96x^73+36x^74+10x^76+2x^104

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 0.36 seconds.