The generator matrix

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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+77x^74+136x^75+212x^76+344x^77+472x^78+650x^79+838x^80+1034x^81+1206x^82+1304x^83+1377x^84+1376x^85+1294x^86+1244x^87+1215x^88+984x^89+815x^90+638x^91+335x^92+308x^93+156x^94+86x^95+89x^96+46x^97+51x^98+32x^99+25x^100+4x^101+20x^102+4x^103+1x^104+2x^106+2x^107+3x^108+2x^110+1x^114

The gray image is a linear code over GF(2) with n=340, k=14 and d=148.
This code was found by Heurico 1.16 in 21.7 seconds.