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

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+52x^70+78x^72+768x^73+72x^74+48x^76+4x^78+1x^144

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 2.94 seconds.