The generator matrix

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

generates a code of length 89 over Z3[X]/(X^2) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+48x^174+150x^175+120x^177+216x^178+50x^180+102x^181+12x^184+4x^186+2x^189+6x^190+12x^195+4x^198+2x^204

The gray image is a linear code over GF(3) with n=267, k=6 and d=174.
This code was found by Heurico 1.16 in 0.137 seconds.