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  0  X  0  X X^2 X^2  X  0  X  0  1  X  1  X X^2 X^2 X^2  1  1  1  X  1  X  1 X^2  1  0  X  1  X  1 X^2  1 X^2  X  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2+X  X X^2  X X^2 X^2+X  0 X^2 X^2  0  X X^2+X  X X^2 X^2+X X^2  X  0 X^2  X X^2+X  X  0  0 X^2  0 X^2  0  X X^2+X  0 X^2  0  X X^2+X  X  0 X^2  X  X X^2  0  X  X  0 X^2 X^2 X^2  0  X X^2+X X^2+X X^2+X  0  0  X  X  X  0  0 X^2 X^2  0  0  X X^2+X  X  X X^2+X
 0  0  X  0  0  0  X X^2+X  X  0  0  0  X  X X^2+X X^2  X X^2+X X^2 X^2+X  X X^2 X^2 X^2  X  0 X^2+X  0  0  0 X^2+X  X  X  X X^2  X  0  X  0 X^2 X^2 X^2+X  0 X^2 X^2  X  0  0  0 X^2  X  X  X  X  X X^2  X  0  0  X  X  X  X X^2 X^2+X  X  0  X X^2  0  X X^2  X  0  X  0  0  X X^2  0  0  0
 0  0  0  X  0  X  X X^2+X  0  X  X X^2  0 X^2 X^2+X  X X^2+X X^2+X X^2+X  X  0  X X^2  0  X  0 X^2 X^2+X  0 X^2 X^2 X^2+X X^2  0  X  X  0  0  X X^2+X  0 X^2 X^2+X  0  0  0 X^2+X X^2+X  X  0  X  X X^2+X X^2+X X^2  0 X^2  X  X X^2 X^2 X^2+X X^2  0 X^2+X  X  X  X X^2  X  0 X^2+X X^2  X X^2 X^2 X^2+X  0  0 X^2+X X^2  0
 0  0  0  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X  X X^2  0  X X^2  0  X  X X^2+X X^2+X  X X^2 X^2  X X^2 X^2+X X^2 X^2+X  0 X^2+X  X X^2+X  X X^2+X X^2  X  X  0 X^2+X  X  0 X^2+X  X  X X^2+X  X X^2 X^2+X  X  X  X  X X^2+X  X X^2  0  0  X  0 X^2 X^2 X^2+X  0  0 X^2 X^2 X^2 X^2 X^2 X^2+X X^2  X  X  X  X  0  X  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 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  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  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 X^2  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+176x^70+4x^71+470x^72+20x^73+728x^74+120x^75+966x^76+316x^77+1311x^78+656x^79+1749x^80+900x^81+1682x^82+964x^83+1607x^84+692x^85+1394x^86+280x^87+918x^88+120x^89+588x^90+20x^91+322x^92+211x^94+4x^95+100x^96+50x^98+8x^100+4x^102+2x^104+1x^116

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 28.3 seconds.