The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+120x^69+278x^70+336x^71+617x^72+516x^73+743x^74+594x^75+778x^76+554x^77+785x^78+560x^79+585x^80+474x^81+409x^82+240x^83+245x^84+118x^85+71x^86+44x^87+68x^88+10x^89+12x^90+14x^91+5x^92+6x^94+4x^95+5x^96

The gray image is a linear code over GF(2) with n=308, k=13 and d=138.
This code was found by Heurico 1.16 in 4.5 seconds.