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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+58x^70+76x^71+174x^72+210x^73+311x^74+400x^75+446x^76+606x^77+674x^78+918x^79+1141x^80+1236x^81+1263x^82+1396x^83+1463x^84+1276x^85+1046x^86+874x^87+649x^88+512x^89+439x^90+306x^91+241x^92+196x^93+133x^94+108x^95+95x^96+50x^97+38x^98+18x^99+14x^100+10x^101+5x^102+1x^122

The gray image is a linear code over GF(2) with n=332, k=14 and d=140.
This code was found by Heurico 1.16 in 28.4 seconds.