The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+134x^80+116x^81+176x^82+128x^83+127x^84+68x^85+91x^86+36x^87+49x^88+8x^89+22x^90+12x^91+7x^92+8x^93+11x^94+16x^96+8x^97+4x^98+1x^104+1x^112

The gray image is a linear code over GF(2) with n=336, k=10 and d=160.
This code was found by Heurico 1.16 in 0.365 seconds.