The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+34x^78+160x^80+154x^82+378x^84+150x^86+70x^88+30x^90+30x^92+16x^94+1x^160

The gray image is a linear code over GF(2) with n=336, k=10 and d=156.
This code was found by Heurico 1.16 in 0.531 seconds.