The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+66x^75+158x^76+256x^77+332x^78+470x^79+768x^80+814x^81+924x^82+1132x^83+1243x^84+1404x^85+1352x^86+1452x^87+1313x^88+1088x^89+995x^90+736x^91+598x^92+416x^93+305x^94+186x^95+103x^96+86x^97+40x^98+48x^99+30x^100+20x^101+16x^102+4x^103+7x^104+12x^105+1x^106+2x^107+2x^108+3x^110+1x^116

The gray image is a linear code over GF(2) with n=344, k=14 and d=150.
This code was found by Heurico 1.16 in 22.5 seconds.