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

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+14x^72+92x^73+14x^74+1x^80+4x^81+1x^82+1x^98

The gray image is a linear code over GF(2) with n=292, k=7 and d=144.
This code was found by Heurico 1.16 in 0.238 seconds.