The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+49x^70+54x^71+156x^72+254x^73+292x^74+490x^75+610x^76+828x^77+1047x^78+1142x^79+1279x^80+1292x^81+1415x^82+1384x^83+1301x^84+1252x^85+957x^86+774x^87+611x^88+386x^89+229x^90+206x^91+104x^92+64x^93+78x^94+46x^95+20x^96+20x^97+21x^98+9x^100+4x^102+5x^104+3x^106+1x^110

The gray image is a linear code over GF(2) with n=328, k=14 and d=140.
This code was found by Heurico 1.16 in 21.6 seconds.