The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+88x^77+179x^78+180x^79+203x^80+244x^81+197x^82+148x^83+158x^84+138x^85+117x^86+86x^87+68x^88+58x^89+44x^90+60x^91+40x^92+8x^93+3x^94+2x^95+4x^96+6x^97+2x^98+4x^99+6x^100+2x^101+1x^102+1x^114

The gray image is a linear code over GF(2) with n=332, k=11 and d=154.
This code was found by Heurico 1.16 in 0.669 seconds.