The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+52x^77+136x^78+116x^79+222x^80+116x^81+196x^82+102x^83+213x^84+116x^85+181x^86+110x^87+181x^88+92x^89+120x^90+50x^91+16x^92+8x^93+2x^94+6x^95+2x^96+2x^98+3x^100+1x^104+2x^106+1x^112+1x^118

The gray image is a linear code over GF(2) with n=336, k=11 and d=154.
This code was found by Heurico 1.16 in 0.864 seconds.