The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+34x^84+82x^85+130x^86+154x^87+244x^88+296x^89+338x^90+426x^91+429x^92+534x^93+606x^94+624x^95+658x^96+666x^97+581x^98+456x^99+405x^100+344x^101+251x^102+196x^103+179x^104+132x^105+79x^106+90x^107+80x^108+46x^109+54x^110+32x^111+18x^112+10x^113+6x^114+4x^115+2x^117+2x^118+2x^119+1x^142

The gray image is a linear code over GF(2) with n=384, k=13 and d=168.
This code was found by Heurico 1.16 in 9.22 seconds.