The generator matrix

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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+206x^65+1163x^66+2864x^67+4785x^68+7834x^69+10346x^70+14416x^71+14917x^72+18184x^73+15229x^74+14482x^75+10396x^76+7592x^77+4202x^78+2438x^79+1154x^80+484x^81+222x^82+78x^83+37x^84+18x^85+4x^86+10x^87+6x^88+2x^89+2x^94

The gray image is a linear code over GF(2) with n=584, k=17 and d=260.
This code was found by Heurico 1.16 in 164 seconds.