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

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+59x^70+128x^71+152x^72+128x^73+31x^74+4x^76+3x^78+3x^80+1x^82+2x^102

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 85.1 seconds.