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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+30x^70+48x^71+289x^72+288x^73+288x^74+48x^75+30x^76+1x^82+1x^138

The gray image is a code over GF(2) with n=584, k=10 and d=280.
This code was found by Heurico 1.16 in 0.531 seconds.