The generator matrix

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

generates a code of length 73 over Z2[X]/(X^3) who�s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+198x^72+36x^76+17x^80+4x^84

The gray image is a linear code over GF(2) with n=292, k=8 and d=144.
This code was found by Heurico 1.16 in 1.51 seconds.