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

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

Homogenous weight enumerator: w(x)=1x^0+33x^74+4x^75+18x^76+4x^77+1x^78+3x^80

The gray image is a code over GF(2) with n=592, k=6 and d=296.
This code was found by Heurico 1.16 in 0.281 seconds.