The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+83x^68+382x^69+602x^70+838x^71+915x^72+1070x^73+1233x^74+1258x^75+1347x^76+1284x^77+1411x^78+1186x^79+1039x^80+1028x^81+807x^82+648x^83+485x^84+312x^85+183x^86+124x^87+55x^88+50x^89+16x^90+10x^91+9x^92+2x^93+4x^94+2x^96

The gray image is a linear code over GF(2) with n=308, k=14 and d=136.
This code was found by Heurico 1.13 in 4.72 seconds.