The generator matrix

 1  0  1  1  1 X^2+X  1  1  2  1  1 X^2+X+2  1 X^2+2  1  1 X+2  1 X^2  X  1  1  1  1  0 X^2+X  1  1  1  1  1 X^2+2  1 X+2  1  1  1  1  2  1  1 X^2+X+2  1  1  1 X^2  X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0  1  1 X^2 X^2+X X^2  X  1
 0  1 X+1 X^2+X X^2+1  1  3  2  1 X^2+X+1 X^2+X+2  1 X^2  1 X^2+3  X  1 X+1  1  1 X^2+X+3 X^2+2 X+2  1  1  1 X+3  1  0 X^2+X X^2+X+1  1 X^2+3  1 X^2+2 X+2  0 X+1  1 X^2+X X^2+1  1 X^2+2 X+2  3  1  1 X^2+X+3 X+3 X+2 X^2+X+3 X^2+3 X^2+1 X^2+3 X+3 X^2+1  1 X+1  1  1 X+1 X+3 X+3 X^2+X+1  0  1  0  1  1  1  1  2  0
 0  0 X^2  0  2  0  2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2  0 X^2+2 X^2+2  0  0 X^2 X^2+2  0  2  2 X^2  2  2 X^2+2 X^2+2  0  0 X^2  2 X^2  2  2  2 X^2  0 X^2 X^2+2  2 X^2+2 X^2 X^2+2  2 X^2 X^2+2  0 X^2  2 X^2+2  0 X^2+2  0  0 X^2 X^2  2  2 X^2+2  2  0 X^2+2 X^2  2 X^2+2 X^2+2  0  2 X^2  0  0  2
 0  0  0  2  2  2  0  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  0  2  2  0  2  2  0  0  2  0  0  2  2  2  0  0  2  0  2  0  2  0  2  2  0  2  2  0  2  2  0  0  0  0  2  0  2  0  0  0  2  0  0  0  2  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+94x^69+265x^70+314x^71+251x^72+308x^73+242x^74+212x^75+189x^76+78x^77+69x^78+16x^79+5x^80+2x^95+1x^100+1x^104

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 0.422 seconds.