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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 X 1 X 1 1 X 1 1 X X X X 0 X 0 0 X 0 0 0 0 1 1
0 X 0 0 X 0 X X 2X 0 0 X X 0 2X X 2X 2X 0 X 2X 0 X 2X 2X 2X 2X 0 0 0 X X 0 X X 2X 0 0 X X 0 2X X 2X 2X 0 X 2X 0 X 2X 2X 2X 2X 0 0 0 X X 0 X X 2X 0 0 X X 0 2X X 2X X 0 X X X 2X 2X 0 X X 2X 2X 0 0 X 0 X 2X X X 0 X 0 X 0 2X 2X
0 0 X 0 2X X 2X X 2X 0 X X 0 2X 0 0 X X 2X 2X 2X 2X X 0 0 X 2X 0 0 X 2X X X 2X 0 2X 0 X X 0 2X 0 0 X X 2X 2X 2X 2X X 0 0 X 2X 0 0 X 2X X X 2X 0 2X 0 X X 0 2X 0 0 X X 2X 2X X 0 2X 0 2X 2X 2X 0 X 0 X X X 0 2X 2X 2X 2X 0 X X 0 0 X
0 0 0 X 2X 2X 0 2X 2X 2X X 0 2X 0 2X X X 0 X X X 2X X 0 X 2X 0 0 X 2X 2X 2X X X X 2X 2X 0 0 0 X X 2X 2X X 0 0 0 2X X 0 2X 0 X 0 X 2X 2X 2X X X X 2X 2X 0 0 0 X X 2X 2X X 2X 2X X 2X X 2X 0 0 X 0 0 X X 2X 0 0 0 2X 0 0 X X 0 X 2X X
generates a code of length 98 over Z3[X]/(X^2) who´s minimum homogenous weight is 193.
Homogenous weight enumerator: w(x)=1x^0+114x^193+44x^195+22x^198+42x^202+8x^204+4x^207+6x^211+2x^240
The gray image is a linear code over GF(3) with n=294, k=5 and d=193.
This code was found by Heurico 1.16 in 1.32 seconds.