The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+88x^75+189x^76+262x^77+386x^78+446x^79+559x^80+634x^81+679x^82+716x^83+646x^84+638x^85+583x^86+562x^87+501x^88+386x^89+318x^90+184x^91+110x^92+102x^93+54x^94+38x^95+32x^96+20x^97+18x^98+12x^99+6x^100+4x^101+9x^102+2x^103+3x^104+1x^108+2x^109+1x^114

The gray image is a linear code over GF(2) with n=336, k=13 and d=150.
This code was found by Heurico 1.16 in 29.5 seconds.