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

generates a code of length 99 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+71x^86+142x^87+244x^88+266x^89+367x^90+406x^91+498x^92+682x^93+689x^94+944x^95+1007x^96+1166x^97+1266x^98+1092x^99+1203x^100+1262x^101+1029x^102+844x^103+740x^104+546x^105+451x^106+356x^107+289x^108+218x^109+154x^110+148x^111+80x^112+70x^113+52x^114+32x^115+25x^116+14x^117+16x^118+2x^119+8x^120+2x^123+1x^124+1x^142

The gray image is a linear code over GF(2) with n=396, k=14 and d=172.
This code was found by Heurico 1.16 in 35.1 seconds.