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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+143x^72+440x^76+256x^78+95x^80+88x^84+1x^152

The gray image is a linear code over GF(2) with n=308, k=10 and d=144.
This code was found by Heurico 1.16 in 0.441 seconds.