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 X^2  X X^2  0  X X^2  X  X  0  X  1  1 X^2  X  1 X^2  1  1  0  1  X  1  X  X  X  X X^2  1  0  1  X X^2  1  X  1  1 X^2  0  1 X^2 X^2  X  1  1  0  1  1  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2+X  X X^2  X X^2 X^2+X  0 X^2 X^2  0  X X^2+X X^2+X X^2  X  0 X^2+X X^2 X^2  0 X^2 X^2+X X^2+X  X X^2  0  0  X X^2 X^2+X X^2+X  0  X X^2+X  X X^2+X  X X^2+X  X  0 X^2+X  X  X X^2  0 X^2  X  0  X  X  X  X  X X^2+X  X X^2+X  X  0  X  0  X X^2+X X^2  0  X  0 X^2  0  X  X  0 X^2+X X^2 X^2  0 X^2  X  0  0  X  X  0  0  0
 0  0  X  0  0  0  X X^2+X  X  0  0  0  X  X X^2+X X^2  X X^2+X X^2 X^2+X  X X^2 X^2 X^2  X  0 X^2+X  0  0 X^2+X X^2+X  0  X  X X^2 X^2  X X^2+X X^2+X X^2  0  X X^2 X^2  0  X X^2+X  0  X  0 X^2+X  0 X^2 X^2 X^2 X^2  0  0 X^2+X X^2+X X^2 X^2+X  0  X X^2+X  X  X  X  0  0  0 X^2+X X^2+X X^2 X^2+X X^2  0 X^2+X X^2  X  X  0 X^2+X  0  X  X  X  X X^2 X^2+X  0 X^2 X^2+X X^2  X  X  X
 0  0  0  X  0  X  X X^2+X  0  X  X X^2  0 X^2 X^2+X  X X^2+X X^2+X X^2+X  X  0  X X^2  0  X X^2+X X^2  0  0 X^2 X^2 X^2 X^2+X X^2+X X^2  0 X^2+X  0  X X^2+X  0 X^2 X^2+X X^2  0  0  X  X  0 X^2+X X^2  X  X X^2+X  0 X^2+X  0  X X^2  X X^2 X^2+X  0  0  0 X^2+X  0 X^2+X X^2+X  0 X^2+X X^2 X^2+X X^2+X X^2  X  X X^2  0 X^2  0  X X^2 X^2+X X^2+X  X  X  X  X X^2 X^2+X X^2+X  X  X  0  0 X^2
 0  0  0  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X  X X^2  0  X X^2  0  X  X X^2+X X^2+X  X X^2+X X^2 X^2 X^2  X  X  0  0 X^2+X X^2+X  X X^2+X X^2  0 X^2+X X^2 X^2  0 X^2+X  X  X X^2  0 X^2 X^2  X  0  0  X  X X^2  X X^2+X X^2 X^2+X X^2+X X^2+X  X  0  X X^2 X^2+X  X  X X^2+X X^2+X X^2+X X^2  X  X  0  X X^2 X^2+X X^2  X  0 X^2  0  0  X  0 X^2  0  0  0 X^2  0  X  X  X X^2+X
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 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  0  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 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  0  0  0 X^2  0 X^2 X^2  0 X^2  0  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  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 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 X^2 X^2  0 X^2
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  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 X^2 X^2 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 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 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 X^2  0 X^2  0  0 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+74x^84+120x^85+197x^86+272x^87+430x^88+426x^89+522x^90+624x^91+739x^92+926x^93+1004x^94+1216x^95+1144x^96+1232x^97+1203x^98+1116x^99+1031x^100+886x^101+741x^102+570x^103+453x^104+348x^105+297x^106+218x^107+141x^108+116x^109+100x^110+62x^111+67x^112+34x^113+25x^114+18x^115+15x^116+8x^117+5x^118+1x^120+1x^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 37.1 seconds.