The generator matrix

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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+98x^68+766x^69+766x^70+1482x^71+735x^72+1298x^73+648x^74+848x^75+383x^76+558x^77+238x^78+182x^79+45x^80+74x^81+25x^82+32x^83+1x^84+8x^85+2x^86+1x^88+1x^90

The gray image is a linear code over GF(2) with n=584, k=13 and d=272.
This code was found by Heurico 1.16 in 2.27 seconds.