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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+30x^70+40x^71+125x^72+152x^73+239x^74+308x^75+371x^76+486x^77+589x^78+744x^79+878x^80+1068x^81+1202x^82+1294x^83+1380x^84+1312x^85+1235x^86+1080x^87+880x^88+752x^89+555x^90+480x^91+314x^92+262x^93+160x^94+136x^95+106x^96+60x^97+62x^98+14x^99+25x^100+4x^101+17x^102+9x^104+4x^106+5x^108+1x^110+1x^112+2x^114+1x^116

The gray image is a linear code over GF(2) with n=336, k=14 and d=140.
This code was found by Heurico 1.16 in 30.2 seconds.