The generator matrix

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

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+157x^74+205x^76+133x^78+9x^80+1x^82+1x^84+1x^86+2x^90+2x^94

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 10.2 seconds.