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.