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^2+X  1  1 X^2 X^2  1  1  0 X^2+X  0  1  1  1  1  1  1 X^2+X X^2+X  1  1  1  1 X^2+X  0  X  1  1  1  1  0  X X^2  X  1  1  1  1  0  1  0  X  0  0  X  1  1  1  1  1  1  X  1  1  1  0  1  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^2+X  1  1 X^2+X  1  1  0  0  1  1 X+1 X+1  1  1  1 X^2+1 X^2+1 X^2 X^2+X+1 X+1 X^2  1  1  X  X X^2  0  1  1  1  1  1 X^2+X  0  1  1  1  1 X^2+X X+1 X+1  1  1  X  0 X^2  X  1  1  X X^2+1  X X^2+X X^2+1  0 X^2 X^2 X+1  1  1 X^2+X  0 X^2+X+1
 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^2+X X^2 X^2  0 X^2+X  0  0  X  X  0  0  0  0 X^2 X^2  0  X  X  X  X X^2 X^2 X^2+X  X  X  X X^2  X  X X^2+X  X X^2 X^2  0  0 X^2 X^2+X X^2+X  0 X^2 X^2+X X^2 X^2+X  X  X X^2+X X^2+X  X X^2+X  0 X^2+X  X X^2+X  X X^2+X X^2  X  0  0  0 X^2+X X^2+X
 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  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 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 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  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  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  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 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 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 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 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  0  0  0  0 X^2  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 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 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 X^2 X^2 X^2 X^2  0 X^2  0 X^2 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+116x^70+24x^71+343x^72+264x^73+606x^74+600x^75+791x^76+976x^77+1078x^78+1432x^79+1226x^80+1592x^81+1229x^82+1432x^83+1068x^84+1032x^85+741x^86+560x^87+486x^88+224x^89+258x^90+48x^91+135x^92+8x^93+53x^94+29x^96+9x^98+14x^100+3x^102+3x^104+2x^106+1x^110

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 71.1 seconds.