The generator matrix

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

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+240x^79+100x^80+388x^81+133x^82+308x^83+96x^84+228x^85+88x^86+108x^87+42x^88+80x^89+26x^90+66x^91+15x^92+58x^93+8x^94+40x^95+1x^96+8x^97+1x^98+6x^99+6x^101+1x^108

The gray image is a linear code over GF(2) with n=336, k=11 and d=158.
This code was found by Heurico 1.11 in 11.3 seconds.