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

generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+17x^74+72x^75+88x^76+40x^77+12x^78+12x^79+5x^80+3x^82+4x^83+2x^84

The gray image is a linear code over GF(2) with n=608, k=8 and d=296.
This code was found by Heurico 1.16 in 0.422 seconds.