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

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+36x^70+54x^71+89x^72+30x^73+27x^74+10x^75+6x^76+2x^85+1x^106

The gray image is a linear code over GF(2) with n=576, k=8 and d=280.
This code was found by Heurico 1.16 in 0.266 seconds.