The generator matrix

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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+248x^71+157x^72+232x^73+157x^74+200x^75+2x^76+24x^77+1x^78+1x^98+1x^110

The gray image is a linear code over GF(2) with n=584, k=10 and d=284.
This code was found by Heurico 1.16 in 5.11 seconds.