The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+128x^67+460x^68+638x^69+1029x^70+1348x^71+1847x^72+1956x^73+2507x^74+2390x^75+2920x^76+2534x^77+2888x^78+2488x^79+2525x^80+1830x^81+1786x^82+1220x^83+900x^84+548x^85+389x^86+200x^87+97x^88+38x^89+35x^90+30x^91+16x^92+8x^93+6x^94+4x^95+2x^96

The gray image is a linear code over GF(2) with n=308, k=15 and d=134.
This code was found by Heurico 1.16 in 52.5 seconds.