The generator matrix

 1  0  0  1  1  1  0  1 X^2  1  1  X X^2+X  1  1 X^2+X  1  1  1  X  0  1  0 X^2+X X^2  1  1  0 X^2+X  1  1 X^2  1 X^2  1  1  1  X  1  1  1  1 X^2+X  1  1  1  X  1  0  1 X^2  0  1  X  X  1  0  1 X^2+X  1  1  1  1  1  1  0  1  0 X^2  1  1 X^2+X  1  X  1  1  1  1  1 X^2+X  1  1  X X^2
 0  1  0  0  1 X^2+1  1  X  1  1 X^2+X  1 X^2 X^2+X+1  0 X^2+X X^2+1 X+1 X^2+X  1 X^2+X X^2+X+1  1  1  1  X  1  1  1 X^2+X  X X^2+X  1  1  1 X^2+1 X^2+X  1 X^2 X^2+X+1  0  0  1 X+1 X^2+X X+1  1 X+1  X X^2  1  0 X+1  1  X  X  1 X^2  X  0 X^2+1 X^2+X  1 X^2 X+1 X^2  X  1  1 X^2  0  1 X^2+1  1 X^2+X+1  0 X^2 X^2+X  0  1 X^2+X X+1  1  1
 0  0  1 X+1 X^2+X+1  0 X+1 X^2+1 X^2+X  1 X^2 X^2+1  1 X^2  1  1  X X^2+X+1  X X^2+X  1 X^2+X X^2+X+1  1 X^2 X+1 X^2+X+1 X^2+1 X^2+X  X  1  1  0 X+1 X^2+1 X^2+X X+1  0 X^2+X+1  1 X^2+X X^2 X+1  X  0  1 X^2+X X^2  1 X^2+1  X  1 X^2+X+1 X+1  1 X^2+X X^2+X X^2  1 X^2+X X^2+X  0 X^2+X X^2+X  1  1 X^2+X X+1  X X^2+X X+1  0 X^2+X X^2+X X^2+1 X^2+X+1 X^2+X  0  X X^2+X X^2+1  1 X+1  1
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2
 0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  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+250x^79+123x^80+344x^81+121x^82+318x^83+109x^84+198x^85+61x^86+176x^87+23x^88+100x^89+30x^90+62x^91+26x^92+46x^93+10x^94+18x^95+4x^96+16x^97+1x^98+8x^99+1x^100+1x^102+1x^104

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 7.81 seconds.