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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+11x^72+132x^73+7x^74+64x^75+2x^76+24x^77+6x^78+2x^80+4x^81+3x^82

The gray image is a linear code over GF(2) with n=592, k=8 and d=288.
This code was found by Heurico 1.16 in 0.391 seconds.