The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+130x^73+131x^74+206x^75+104x^76+118x^77+39x^78+68x^79+48x^80+46x^81+35x^82+38x^83+21x^84+4x^85+2x^86+16x^87+1x^88+4x^89+8x^91+2x^93+1x^94+1x^100

The gray image is a linear code over GF(2) with n=308, k=10 and d=146.
This code was found by Heurico 1.11 in 0.204 seconds.