The generator matrix

 1  0  1  1  1  0  1 X^2+X  1  1 X^2+X  1  1 X^2  1  1  0  1  1  X  1  1  1 X^2+X  1 X^2+X  1  1  1  1  X  1  1  1  1  1 X^2  1  X  1  1  1  1  1  X  1 X^2+X  1  0  1  0 X^2  1  1 X^2  X  1  X  0  1 X^2+X  1  1  1  1  1 X^2+X  1  1  1  1 X^2  1  0  1  1  1
 0  1  1  0 X^2+X+1  1  X  1 X^2+X+1  X  1  1 X^2  1 X+1 X^2+X  1 X+1  0  1  X X+1  1  1  1  1 X^2+1  X X^2+X+1 X^2  1 X^2+X+1 X^2  X X^2+X+1  1  1  0  1 X^2+X X^2+1  X  1 X+1  1  X  1 X^2+1  1  0  1  X  0 X^2+X+1  X  1 X^2 X^2+X  1 X^2+1  1 X^2+X+1 X+1  1  0  1  1 X+1  1  1 X^2+1  1 X^2+X+1  1  X X^2+X+1 X^2
 0  0  X  0 X^2+X  X  0  X  0  X  0 X^2 X^2+X  X  X  X  0 X^2  X X^2+X X^2 X^2 X^2+X X^2  0 X^2+X X^2  0  X X^2+X  X X^2  0 X^2+X  X X^2+X  0  0  0  0 X^2+X X^2  X X^2  0  X  X X^2 X^2 X^2+X X^2+X  X  0  X X^2+X  0 X^2  X  X  0 X^2+X X^2 X^2+X X^2+X X^2  0 X^2+X X^2 X^2  X  0 X^2  X X^2 X^2 X^2+X X^2
 0  0  0  X  0  X  X  X X^2+X  0 X^2  X X^2 X^2 X^2+X  X  X  0 X^2+X X^2  0 X^2+X  0 X^2+X X^2  X X^2 X^2+X  X X^2 X^2 X^2+X  X  0 X^2  0  X  0 X^2+X  0  X X^2+X X^2+X  0  0  X  X  X X^2 X^2+X X^2+X X^2 X^2+X X^2+X  X  X X^2  0 X^2 X^2+X X^2  X  X X^2 X^2+X  X  0 X^2  0  0 X^2+X X^2 X^2+X  X X^2 X^2  X
 0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 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 71.

Homogenous weight enumerator: w(x)=1x^0+84x^71+130x^72+264x^73+166x^74+252x^75+100x^76+208x^77+151x^78+182x^79+96x^80+150x^81+52x^82+76x^83+50x^84+40x^85+11x^86+4x^87+5x^88+8x^89+2x^90+8x^91+2x^95+2x^97+2x^98+2x^104

The gray image is a linear code over GF(2) with n=308, k=11 and d=142.
This code was found by Heurico 1.16 in 0.547 seconds.