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

generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+38x^74+192x^75+12x^76+8x^78+2x^88+2x^90+1x^96

The gray image is a code over GF(2) with n=600, k=8 and d=296.
This code was found by Heurico 1.16 in 0.469 seconds.