The generator matrix

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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+82x^36+168x^39+456x^42+30x^43+18x^44+1020x^45+240x^46+216x^47+1730x^48+900x^49+1080x^50+3762x^51+2190x^52+2880x^53+6776x^54+3606x^55+4320x^56+8544x^57+3636x^58+3456x^59+6330x^60+1992x^61+1152x^62+2420x^63+528x^64+1008x^66+294x^69+150x^72+52x^75+12x^78

The gray image is a linear code over GF(3) with n=84, k=10 and d=36.
This code was found by Heurico 1.16 in 13 seconds.