The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1  1  X X^2+X  0  1  X  X X^2  1  1  1  X  1  1  1 X^2+X X^2+X  X X^2  1  1  1  1  0  1 X^2  1  0  1  1  X  1 X^2+X  1 X^2+X  1 X^2+X  X X^2  1  X  1  X  1  0  1 X^2+X  1  0  X  1  1 X^2+X X^2  1  1  1  1 X^2  1  1 X^2  1  1  1 X^2+X  X  X X^2  1  0  1
 0  1  0  0  0  0  0  0 X^2  1  1 X^2+1  1  1  1  1 X^2+X X^2+X  1  X  X X^2+X+1  1 X^2+X  1  0 X+1  1  1  1  1 X^2 X+1  1 X+1  1  0 X^2+X X^2 X^2+X  1 X^2 X^2+X X^2+X  1  1 X^2+X X^2+X  1 X^2  X  X X^2  1  X  X  X X^2+X  1 X^2+X+1  1  1  0 X^2+X X^2  0 X^2+X+1 X+1  X X^2+1  X X^2+X  1  1 X+1 X+1 X^2+1  1  1 X^2+X  1  1  X  0
 0  0  1  0  0  0  1  1  1  1 X^2+1 X^2  X X^2+1 X^2+1 X^2 X^2  0 X^2+X+1  1  1 X+1 X^2+X  1 X^2+X+1  0 X^2 X^2+1  X X^2+X  1  1  X X+1 X^2+X X+1  X  X X^2  1  0 X^2+X+1  1 X^2+X+1 X^2+X X^2+X+1  1  0 X^2+X X^2+X  1  1  1 X+1 X^2+X  1  1 X^2+X+1 X^2  X X^2 X+1  0  X  0  1 X^2+1  0 X+1 X+1  1 X^2 X^2 X^2 X^2+1  0  X X^2+X X^2+1  1 X^2+X  X X^2 X^2
 0  0  0  1  0  1  1 X^2 X^2+1 X^2 X^2+1  1 X^2 X+1 X^2+X X+1 X+1  1 X^2  X  X X^2 X+1 X^2+1 X+1  0  0 X^2+1  0 X^2+X+1 X^2+X X^2+1 X^2 X+1 X+1  1 X^2+X+1  1 X+1  0 X^2+X X^2+1 X+1 X^2+X+1 X^2+X  0  1 X^2 X^2+1  1 X^2+X X^2 X^2+X  X  X  0  1  1 X+1  X X^2+X X^2 X^2+X+1  0 X^2+X X^2 X^2+1 X^2+X  0 X^2 X^2+X  1  X X+1 X+1 X^2+X+1 X^2+1 X^2+X+1 X^2 X^2 X^2+X  X  1  0
 0  0  0  0  1  1 X^2 X^2+1 X^2+1  0  1  0 X+1 X^2 X^2+1 X^2+X+1  0 X^2+1  0 X^2+1 X^2 X^2+X+1 X^2+1  X  X X+1 X^2+X X+1 X^2+1  X X+1 X+1 X^2  1  1 X+1 X^2+X X^2+X X^2+X+1 X^2  1  1  0 X^2+X  X X+1 X+1 X+1 X+1  1  0  0 X+1  1  1  1 X^2  X  0  0 X^2+X  1  X  X  1 X^2+X+1  0 X+1  0  X  X X^2+X X^2+X+1 X^2 X+1 X^2+X  X X^2+X+1  0  X X+1 X+1  X X^2+X
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 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  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 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 X^2 X^2 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+154x^73+540x^74+1096x^75+1640x^76+2072x^77+2751x^78+3364x^79+3695x^80+4372x^81+4903x^82+5278x^83+5543x^84+5394x^85+5240x^86+4638x^87+3781x^88+3260x^89+2663x^90+1872x^91+1307x^92+862x^93+498x^94+304x^95+143x^96+66x^97+40x^98+18x^99+16x^100+8x^101+3x^102+6x^103+4x^105+2x^106+2x^108

The gray image is a linear code over GF(2) with n=336, k=16 and d=146.
This code was found by Heurico 1.13 in 70.8 seconds.