The generator matrix

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

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+130x^68+20x^69+208x^70+68x^71+397x^72+128x^73+406x^74+192x^75+487x^76+216x^77+440x^78+184x^79+388x^80+128x^81+242x^82+64x^83+154x^84+20x^85+78x^86+4x^87+80x^88+32x^90+19x^92+2x^94+5x^96+1x^100+1x^104+1x^116

The gray image is a linear code over GF(2) with n=308, k=12 and d=136.
This code was found by Heurico 1.16 in 1.84 seconds.