The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+109x^70+56x^71+355x^72+272x^73+587x^74+588x^75+871x^76+956x^77+1082x^78+1328x^79+1182x^80+1608x^81+1211x^82+1544x^83+1045x^84+1040x^85+750x^86+536x^87+438x^88+200x^89+254x^90+44x^91+159x^92+20x^93+82x^94+37x^96+19x^98+3x^100+1x^102+3x^104+1x^106+2x^108

The gray image is a linear code over GF(2) with n=324, k=14 and d=140.
This code was found by Heurico 1.16 in 20.2 seconds.