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

generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+162x^51+424x^54+712x^57+1128x^60+2070x^63+5146x^66+11164x^69+15668x^72+12984x^75+5916x^78+1690x^81+998x^84+546x^87+306x^90+86x^93+38x^96+10x^99

The gray image is a linear code over GF(3) with n=108, k=10 and d=51.
This code was found by Heurico 1.16 in 38.1 seconds.