The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+54x^73+107x^74+274x^75+292x^76+556x^77+576x^78+994x^79+772x^80+1492x^81+854x^82+1874x^83+1012x^84+1750x^85+911x^86+1380x^87+702x^88+1016x^89+493x^90+476x^91+232x^92+194x^93+100x^94+96x^95+42x^96+54x^97+26x^98+24x^99+14x^100+4x^101+5x^102+2x^103+2x^104+2x^108+1x^112

The gray image is a linear code over GF(2) with n=336, k=14 and d=146.
This code was found by Heurico 1.16 in 21.2 seconds.