The generator matrix

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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+244x^69+76x^70+220x^71+132x^72+736x^73+96x^74+224x^75+56x^76+236x^77+20x^78+4x^79+1x^80+1x^96+1x^112

The gray image is a code over GF(2) with n=584, k=11 and d=276.
This code was found by Heurico 1.16 in 0.296 seconds.