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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+70x^73+148x^74+14x^75+6x^76+6x^77+4x^78+2x^79+1x^88+4x^89

The gray image is a linear code over GF(2) with n=592, k=8 and d=292.
This code was found by Heurico 1.16 in 11.3 seconds.