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

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+145x^84+346x^86+717x^88+1030x^90+1535x^92+1980x^94+2578x^96+2466x^98+2081x^100+1394x^102+898x^104+512x^106+358x^108+164x^110+104x^112+38x^114+22x^116+4x^118+5x^120+2x^122+2x^124+1x^128+1x^140

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 37.3 seconds.