The generator matrix

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

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+325x^70+406x^71+253x^72+294x^73+170x^74+254x^75+186x^76+58x^77+67x^78+12x^79+12x^80+4x^84+4x^86+2x^102

The gray image is a code over GF(2) with n=584, k=11 and d=280.
This code was found by Heurico 1.16 in 0.297 seconds.