The generator matrix

 1  0  1  1  1 X^2  1  1  X  1  1 X^2+X  1  1  X  1  1 X^2 X^2+X  1  1  1  1  0  X  X  X X^2  0  1  1  1  0  1  1  0 X^2+X  1  1 X^2+X  1  0 X^2  0  1  1  1  1  1  X  1  1  1  1  0  X X^2+X  X X^2  1  1  1  1  1  X  1 X^2  0  0 X^2  1  1  1  1  1 X^2  1
 0  1  1  0 X+1  1 X^2+X+1  0  1 X^2  1  1  X X^2+1  1  X X+1  1  1 X^2+X X+1  X  1  1  1  1  1  1  1  0 X^2+1 X^2  1 X+1 X^2+X+1  1  1  0 X^2+1  1 X^2  0  1  1  X X^2+X  1 X+1  X X^2 X^2+1 X^2+X+1 X^2 X^2+X  X  1  1  1  1 X^2+1 X^2+X  0 X^2 X^2+1 X^2+X  0  1  1  1  1 X^2+1 X^2+1 X^2+X+1  0 X^2+X X^2  0
 0  0  X  0  0  0  0  X X^2+X  X  X  X X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2+X X^2 X^2 X^2 X^2+X  0 X^2  X X^2+X  0  0 X^2+X X^2+X X^2+X X^2 X^2+X  0 X^2+X  X X^2  0 X^2  X X^2+X  X  X  0 X^2 X^2  X  X  X X^2  0  X  0  0  0 X^2  0  X  X X^2 X^2  0  0 X^2+X X^2 X^2  X X^2+X  X X^2 X^2+X  X  X X^2
 0  0  0  X X^2 X^2+X X^2+X  X X^2 X^2 X^2+X  X  0  0  0 X^2+X  X X^2+X X^2+X X^2+X X^2 X^2  X X^2  X  X  0  0 X^2 X^2  0  0  X X^2+X  X X^2+X X^2  X  0  X  X  X X^2+X  0 X^2 X^2+X X^2+X X^2  0 X^2+X  X X^2+X  X  X  0 X^2  X  0  X X^2  0 X^2+X  0 X^2+X  X X^2+X X^2  0  X X^2  X X^2 X^2+X X^2 X^2  X 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+44x^72+136x^73+129x^74+122x^75+94x^76+78x^77+114x^78+74x^79+66x^80+38x^81+30x^82+38x^83+18x^84+14x^85+11x^86+6x^87+2x^89+1x^90+4x^93+2x^94+1x^96+1x^102

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 0.282 seconds.