The generator matrix

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

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+34x^72+96x^73+143x^74+118x^75+133x^76+156x^77+68x^78+50x^79+57x^80+52x^81+35x^82+20x^83+25x^84+12x^85+4x^86+2x^87+6x^88+4x^89+4x^90+2x^91+2x^110

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 0.358 seconds.