The generator matrix

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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+30x^70+102x^71+259x^72+248x^73+251x^74+96x^75+28x^76+6x^78+2x^79+1x^130

The gray image is a linear code over GF(2) with n=584, k=10 and d=280.
This code was found by Heurico 1.16 in 0.25 seconds.