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

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+104x^36+360x^39+668x^42+976x^45+1662x^48+2348x^51+16016x^54+29412x^57+2934x^60+2152x^63+1332x^66+670x^69+266x^72+120x^75+22x^78+6x^81

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 22.2 seconds.