The generator matrix

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

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+82x^75+165x^76+294x^77+395x^78+462x^79+580x^80+612x^81+617x^82+678x^83+684x^84+604x^85+637x^86+574x^87+492x^88+436x^89+319x^90+206x^91+94x^92+66x^93+38x^94+34x^95+41x^96+24x^97+8x^98+10x^99+20x^100+12x^101+2x^103+2x^104+1x^108+2x^110

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 6.47 seconds.