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

generates a code of length 75 over Z4[X]/(X^3+2,2X) who�s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+60x^76+3x^80

The gray image is a code over GF(2) with n=600, k=6 and d=304.
This code was found by Heurico 1.16 in 0.265 seconds.