The generator matrix

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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+82x^74+80x^75+236x^76+16x^77+44x^78+24x^79+19x^80+2x^82+8x^83

The gray image is a code over GF(2) with n=608, k=9 and d=296.
This code was found by Heurico 1.16 in 0.281 seconds.