The generator matrix

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

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+104x^69+256x^70+470x^71+490x^72+650x^73+546x^74+784x^75+532x^76+770x^77+614x^78+774x^79+482x^80+472x^81+344x^82+300x^83+176x^84+180x^85+89x^86+82x^87+41x^88+8x^89+2x^90+4x^91+2x^92+6x^93+3x^94+2x^95+4x^96+2x^97+2x^98

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 4.49 seconds.