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 X X 1 1 1 1 X X 1 X 1 0 X X 1 1 X X X 0 X X X X 0 0 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 X X 0 0 X X X 2X 2X X 2X X 2X X 2X 2X 0 0 X X 0 0 0 2X X 0 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 2X 2X 2X 2X X 2X 2X 0 0 X 0 X X X 2X X 2X 0 X 2X X 0 0 2X 0 0
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 X 0 0 2X 0 X 2X X 2X X X 0 2X 0 2X X 2X 2X 2X 2X X X 2X X 2X X 0
generates a code of length 97 over Z3[X]/(X^2) who´s minimum homogenous weight is 191.
Homogenous weight enumerator: w(x)=1x^0+114x^191+26x^192+36x^195+4x^198+42x^200+8x^201+4x^207+6x^209+2x^237
The gray image is a linear code over GF(3) with n=291, k=5 and d=191.
This code was found by Heurico 1.16 in 1.11 seconds.