The generator matrix

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

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+73x^68+336x^69+281x^70+284x^71+239x^72+232x^73+197x^74+240x^75+70x^76+54x^77+30x^78+4x^79+2x^82+1x^86+1x^90+1x^92+2x^93

The gray image is a linear code over GF(2) with n=576, k=11 and d=272.
This code was found by Heurico 1.16 in 0.422 seconds.