The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+64x^70+242x^71+228x^72+448x^73+273x^74+464x^75+277x^76+450x^77+257x^78+420x^79+138x^80+206x^81+124x^82+174x^83+107x^84+80x^85+39x^86+56x^87+12x^88+14x^89+9x^90+2x^91+2x^92+2x^93+2x^94+2x^95+3x^96

The gray image is a linear code over GF(2) with n=308, k=12 and d=140.
This code was found by Heurico 1.16 in 1.12 seconds.