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  X  X  X  1  1  1  1  1  1  1  1  X  X  X  X  X  X X^2  0  X  X X^2  0  1 X^2 X^2 X^2 X^2  1 X^3 X^3  1  1 X^2  1  X  1  1  1  X  X  X  X  X  1  1  1
 0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 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 X^2 X^2  0 X^3  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 X^2  0 X^3 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2  0  0 X^3 X^2 X^2 X^3 X^2 X^2  0 X^3 X^3 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3  0 X^3  0 X^3  0 X^3+X^2  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 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 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+26x^73+71x^74+8x^75+7x^76+10x^77+4x^83+1x^86

The gray image is a linear code over GF(2) with n=592, k=7 and d=292.
This code was found by Heurico 1.16 in 0.391 seconds.