The generator matrix

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

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+46x^69+102x^70+196x^71+279x^72+336x^73+332x^74+330x^75+344x^76+322x^77+346x^78+336x^79+265x^80+256x^81+226x^82+124x^83+115x^84+44x^85+16x^86+16x^87+12x^88+14x^89+2x^90+18x^91+4x^92+4x^93+4x^95+2x^96+2x^97+1x^100+1x^104

The gray image is a linear code over GF(2) with n=308, k=12 and d=138.
This code was found by Heurico 1.16 in 1.33 seconds.