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

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+150x^70+4x^71+463x^72+40x^73+744x^74+132x^75+998x^76+416x^77+1392x^78+640x^79+1602x^80+804x^81+1728x^82+860x^83+1714x^84+644x^85+1214x^86+360x^87+955x^88+132x^89+624x^90+48x^91+364x^92+12x^93+176x^94+4x^95+98x^96+48x^98+12x^100+4x^102+1x^112

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 28.7 seconds.