The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^2+X  1  1 X^2+X X^2  1  1  1  1 X^3+X  1 X^3+X^2 X^3+X^2+X  1  1 X^3+X^2+X X^2  1 X^2  X X^3+X  1  1  0  1  1 X^3+X  X  1  1 X^3+X X^3+X^2  1  1  X X^3+X  1  1  1  1  1  1 X^2  1 X^3+X^2  1 X^3+X^2  1  1  1  1 X^2  1 X^2+X X^2 X^2+X  1  1  1 X^3+X X^2+X X^3+X  1  1  1  1 X^3+X^2+X  1 X^3+X^2+X X^2+X  1  0  1  1 X^3 X^3+X^2+X  1  1  1 X^2  X X^2+X  1  1  1  1
 0  1  0  0  0 X^3+1 X^3+1  1 X^3+X^2+X X^3+X X^3+X^2+X X+1 X^2+1  1  1 X+1 X^3+X^2+X  X X+1  1 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3 X^2+1  1 X^3 X^2+X+1  1  1 X^2  0  1  1 X^3 X+1 X^3+X^2  1 X^3+X X^3+1  1 X^3+X X^3+X^2+1 X^2+X+1  1  1 X^3  0 X^3+X^2+X+1 X^3+X^2 X^3+X^2+X+1 X^3  1 X^3+X^2+X+1  1  X X^3+X^2 X^2+1 X^3+X+1 X^3+X^2+X X^3+1  1 X^3+X^2  0  1  1  X X^2+1  0  X  1  1 X^3+X X^3+X X^3+X^2  0  0 X^2+X+1  1  1  1  1 X^2+X+1 X^3+X^2+X X^3+X X^3+X^2 X^2+X X^2+X+1 X^3 X^2+X X^2+X  1 X+1 X^3  0  0
 0  0  1  0  1  1 X^2 X^2+1  0 X^3+1  1 X^2+1  X X^3+X X^3+X^2+X+1 X^2+X X^2+X+1 X^2+X X^3+X+1  1  0  1  1  1 X^2+X+1 X^3+1 X^3+X^2+X X^3+X^2 X^3+X X^2  1 X^2+X+1 X+1 X^3  X X^3+X+1 X^3+X^2  X  X  X X^3+X^2+1  1 X^2+1 X^2 X^3+X+1 X^2+X+1 X^2+X+1 X^3 X^2+1  0 X^3+X^2+X+1 X^2 X+1 X^3 X+1 X^3+X^2+1  1  0 X^3+X X^3+X^2+1 X^3+1 X^2 X+1  1 X^3+X^2 X^2+X X^3 X^3+X^2 X^3+X^2+X  1 X+1  0 X^3+X^2+X X^2 X+1 X^3+X+1  1 X^2+X X^3+X  0 X+1 X^3+1 X^2+1 X^3+X+1 X^2+X X^3+X X^3+X X^3+X^2+1 X^3+1  1 X^3+X^2+X X^3+X^2+X X^2+1 X^3  0  0
 0  0  0  1  1 X^2 X^2+1  1 X^2+X+1 X^3+X X^2+1 X^2+1 X^2 X^3+1  X X^3+X^2+X+1 X^3+X^2+1 X^2 X^2+X+1 X^3+X+1 X^3+X^2+1 X^3+X^2+1 X^3+X^2 X^3  X  X  1 X^2+X  0 X^3+X^2+X+1 X^2+1 X^3+X^2+X X+1 X^3+X^2+X X^3+X X^3+X  1 X^2+1 X^2+X+1 X^2+X+1 X^2+X X^3+X^2+X X^3+X+1 X^3+X X^3+X X^3+X^2+X+1 X^2+X+1 X^3+X^2+X X^3+X+1  1 X^3+X^2 X+1 X^3+X^2+X+1 X^3+X^2 X^2 X^2+X X^2+X+1 X^2 X^2+1 X^2 X^3+X^2 X^3 X^2+X+1 X^2  1  0 X^2+X X^3 X^3+1  X X^2+X+1 X^3+1  1 X^2  0 X^3+X^2 X^3+X+1 X^2+X X^2 X^3+X+1  0 X+1 X^2+X  0  1  1 X^3+X^2+X+1  0 X^3+X^2+X X+1  1 X^3 X^2+X  0  0  0
 0  0  0  0 X^3+X^2  0 X^3+X^2  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0  0 X^2  0 X^3 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0  0 X^3+X^2 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3 X^3 X^3+X^2 X^2 X^3  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3  0  0

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+64x^84+126x^85+427x^86+1198x^87+2454x^88+4298x^89+8100x^90+10726x^91+15783x^92+19756x^93+25355x^94+27164x^95+30483x^96+27766x^97+26207x^98+20374x^99+15925x^100+10048x^101+7112x^102+3820x^103+2386x^104+1276x^105+665x^106+338x^107+127x^108+48x^109+64x^110+22x^111+8x^112+8x^113+4x^114+6x^115+1x^116+2x^117+2x^118

The gray image is a linear code over GF(2) with n=768, k=18 and d=336.
This code was found by Heurico 1.16 in 889 seconds.