The generator matrix

1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 0 1 1 0 1 0 1 X X X 1 X 1 1 0 1 X 1 1 1 X 1 0 0 0 X X 1 1 0 X X X 1 0 0 1 0 1 1 1 X X X X X 1 0 X 0 X 1 1 1 1 X 0 1 1 1 1 1 X X 1 X 0 1 1 1 1 1 X 1 1 0 1 1 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X 1 X+1 1 1 1 1 X+1 1 1 1 X+1 0 X+1 X+1 1 X+1 0 0 1 1 1 X X 1 X X 1 1 0 1 1 1 1 1 1 1 0 0 X X X X 1 1 0 1 1 1 X 0 1 X+1 1 X+1 X 1 X X 1 X+1 1 0 1 1 X 1 X X 0 0 X+1 0 0 X+1 X X 1 0 X 0
0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 X X X X 0 X X X 0 X 0 X 1 1 1 1 1 X+1 1 X+1 1 1 1 X+1 1 X+1 0 X+1 1 X+1 X+1 1 X+1 1 0 1 1 X X+1 1 1 X+1 1 1 X 1 X+1 X X X+1 X+1 1 0 1 X+1 1 0 0 X+1 X+1 X X 1 0 X+1 X+1 1 1 X X+1 0 X 1 X+1 X 0
0 0 0 1 0 0 0 0 0 X X 1 1 1 1 X+1 1 1 X X+1 1 0 X X+1 X X X+1 X+1 1 0 0 1 1 1 0 1 X 0 1 X X+1 1 1 X+1 1 X+1 0 X X+1 1 X+1 X X+1 X+1 1 0 0 X X 0 0 X 1 0 X 1 0 X X X+1 X 1 0 0 X 1 X 1 1 1 X+1 X+1 X X X+1 X+1 1 X+1 X+1 1 X+1 1 1 1 X+1 X 0
0 0 0 0 1 0 0 1 X 1 1 0 X+1 1 0 1 0 1 X 1 X+1 0 0 X 1 1 X 0 X+1 1 X+1 X X+1 0 X+1 X X+1 X 1 1 1 X 1 0 X+1 X+1 0 1 1 X 1 1 0 X+1 X X 0 X 1 0 1 0 1 0 0 X+1 X+1 X+1 0 0 1 0 X+1 1 X X+1 0 1 X X+1 X X+1 X+1 0 X+1 X+1 1 1 X X X+1 0 X 0 X X 0
0 0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 X X+1 1 1 0 1 X+1 X 1 X+1 X X X 1 0 X X+1 X X+1 X 1 X 0 0 X 1 0 1 1 0 0 X+1 X+1 X X+1 0 1 X 1 0 1 0 X X 1 1 X+1 0 0 0 0 0 1 X X+1 1 1 0 X X 0 0 1 X+1 0 1 X+1 X+1 X 0 1 0 1 X X+1 X X X 1 0
0 0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 0 X X+1 0 0 0 X+1 1 1 1 1 X 0 X X+1 0 1 1 X+1 X 0 X 1 0 1 X+1 1 1 1 0 1 X X+1 X+1 0 1 X 1 X X X+1 1 0 0 X+1 0 X+1 0 X+1 1 0 X X X+1 X 0 0 X X+1 X X+1 X+1 1 0 0 X+1 X 1 0 X+1 0 0 X X X X+1 X+1 0 0 0 X+1 0 0

generates a code of length 97 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+74x^82+104x^83+204x^84+284x^85+397x^86+478x^87+566x^88+576x^89+602x^90+672x^91+709x^92+798x^93+768x^94+838x^95+802x^96+822x^97+807x^98+800x^99+761x^100+802x^101+702x^102+640x^103+629x^104+544x^105+495x^106+354x^107+300x^108+242x^109+189x^110+116x^111+118x^112+82x^113+58x^114+22x^115+6x^116+10x^117+3x^118+8x^119+1x^134

The gray image is a linear code over GF(2) with n=194, k=14 and d=82.
This code was found by Heurico 1.10 in 18.7 seconds.