The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+164x^77+558x^78+838x^79+1259x^80+1386x^81+1921x^82+1960x^83+2318x^84+2302x^85+2665x^86+2272x^87+2882x^88+2202x^89+2264x^90+1892x^91+1720x^92+1304x^93+1114x^94+702x^95+472x^96+232x^97+151x^98+76x^99+48x^100+20x^101+31x^102+4x^103+2x^104+4x^105+2x^108+2x^109

The gray image is a linear code over GF(2) with n=348, k=15 and d=154.
This code was found by Heurico 1.16 in 57 seconds.