The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+152x^76+64x^77+312x^78+268x^79+660x^80+640x^81+748x^82+972x^83+1180x^84+1272x^85+1176x^86+1632x^87+1151x^88+1464x^89+1026x^90+960x^91+782x^92+616x^93+408x^94+244x^95+302x^96+40x^97+128x^98+20x^99+80x^100+40x^102+25x^104+2x^106+14x^108+5x^112

The gray image is a linear code over GF(2) with n=348, k=14 and d=152.
This code was found by Heurico 1.16 in 22.9 seconds.