The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  X  1  1 X^2+2  1  1  2  1  1 X^2+X  1  1 X^2  1  1 X+2  1  1  1  0  1 X^2+X+2  1  1  X  1  1 X^2+2  1  1  1  1  1  1  1  1  0 X^2+X+2 X^2+2  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X
 0  1 X+1 X^2+X+2 X^2+1  1  X X^2+X+1  1 X^2+2  3  1  2 X+1  1 X^2+X X^2+3  1 X+2 X^2+X+3  1 X^2  1  1  0 X^2+X+2 X+1  1  1  1 X^2+2 X^2+X+3  1  X X^2+3  1  2 X^2+X X^2+2  X X+3 X^2+3 X^2+X+3  1  1  1  1  1  0 X^2+X+2  0 X^2+X+2 X^2 X+2 X^2 X+2 X^2 X+2 X^2+2  X  2 X^2+X  2 X^2+X X+3 X+3 X^2+1 X^2+X+1 X^2+X+2 X^2+1 X^2+3  2  2
 0  0 X^2 X^2+2  2 X^2 X^2 X^2+2 X^2+2  2  0  2 X^2  0 X^2  0 X^2  0  2  2 X^2+2 X^2+2 X^2+2  2  2 X^2  2  2 X^2 X^2+2  0  0 X^2 X^2+2 X^2+2  0 X^2+2  2 X^2  0 X^2+2  0 X^2  2 X^2+2  2 X^2  0 X^2+2  2 X^2  0  2 X^2+2  0 X^2 X^2  0 X^2+2  2  2 X^2+2  0 X^2  2  0 X^2+2 X^2 X^2  0  2 X^2 X^2

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+248x^71+157x^72+232x^73+157x^74+200x^75+2x^76+24x^77+1x^78+1x^98+1x^110

The gray image is a code over GF(2) with n=584, k=10 and d=284.
This code was found by Heurico 1.16 in 0.922 seconds.