The generator matrix

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

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+150x^73+68x^74+202x^75+78x^76+198x^77+65x^78+104x^79+15x^80+62x^81+13x^82+6x^83+10x^85+9x^86+12x^87+1x^88+12x^89+4x^90+12x^91+1x^96+1x^98

The gray image is a linear code over GF(2) with n=308, k=10 and d=146.
This code was found by Heurico 1.16 in 1.88 seconds.