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 X^3 X^2 X^3 X^2 X^3 X^2 X^3  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2  0 X^3 X^2  0 X^3 X^2 X^2  0 X^3 X^2  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3  0 X^3  0 X^3  0 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^3+X^2
 0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3

generates a code of length 75 over Z2[X]/(X^4) 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 linear code over GF(2) with n=600, k=8 and d=296.
This code was found by Heurico 1.16 in 0.485 seconds.