The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+29x^74+78x^75+206x^76+216x^77+454x^78+340x^79+727x^80+446x^81+780x^82+498x^83+811x^84+472x^85+838x^86+438x^87+630x^88+308x^89+373x^90+144x^91+145x^92+70x^93+60x^94+30x^95+22x^96+20x^97+15x^98+8x^99+13x^100+2x^101+6x^102+4x^104+2x^105+2x^106+1x^108+2x^110+1x^114

The gray image is a linear code over GF(2) with n=336, k=13 and d=148.
This code was found by Heurico 1.16 in 6.16 seconds.