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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1 X^2 X^2  1 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  1  1
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  0  2 X^2 X^2+2  0  2 X^2 X^2+2  2  0 X^2+2 X^2  2  0 X^2+2 X^2  2  0 X^2+2 X^2 X^2 X^2 X^2+2 X^2+2  2  0 X^2+2 X^2  0  0  2  2  0  2 X^2 X^2+2  0  2 X^2 X^2+2  2  0 X^2  0 X^2+2 X^2+2 X^2+2  2  0  2  2 X^2 X^2+2  0 X^2 X^2  2 X^2+2 X^2+2
 0  0 X^2+2 X^2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  0 X^2+2 X^2  0  0 X^2 X^2  0  2 X^2+2 X^2+2  2  2 X^2+2 X^2+2  2  0 X^2 X^2  0 X^2 X^2+2  0  2 X^2 X^2+2 X^2+2 X^2 X^2+2 X^2  2  0  0  2  2  0  0 X^2 X^2  0  2 X^2+2 X^2+2  2  2 X^2+2 X^2 X^2+2 X^2  0  2 X^2 X^2  2  0 X^2+2 X^2+2  2  2  0 X^2+2 X^2+2 X^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+68x^74+144x^75+14x^76+16x^77+8x^78+1x^88+4x^90

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 1.97 seconds.