The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+222x^79+121x^80+366x^81+114x^82+348x^83+110x^84+200x^85+74x^86+162x^87+29x^88+94x^89+25x^90+62x^91+21x^92+28x^93+10x^94+18x^95+1x^96+16x^97+18x^99+5x^100+2x^103+1x^106

The gray image is a linear code over GF(2) with n=336, k=11 and d=158.
This code was found by Heurico 1.16 in 2.16 seconds.