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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+47x^84+138x^85+199x^86+260x^87+420x^88+436x^89+611x^90+678x^91+713x^92+882x^93+1000x^94+1116x^95+1118x^96+1266x^97+1184x^98+1138x^99+1088x^100+850x^101+675x^102+636x^103+473x^104+362x^105+274x^106+184x^107+168x^108+120x^109+133x^110+74x^111+56x^112+40x^113+13x^114+8x^115+12x^116+2x^117+4x^118+2x^119+2x^122+1x^134

The gray image is a linear code over GF(2) with n=388, k=14 and d=168.
This code was found by Heurico 1.16 in 36.5 seconds.