The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+280x^78+129x^80+308x^82+104x^84+124x^86+12x^88+44x^90+8x^92+8x^94+1x^96+4x^110+1x^112

The gray image is a linear code over GF(2) with n=328, k=10 and d=156.
This code was found by Heurico 1.16 in 77.3 seconds.