The generator matrix

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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+86x^39+42x^41+406x^42+168x^43+216x^44+1598x^45+618x^46+864x^47+3390x^48+1602x^49+2310x^50+6056x^51+3246x^52+3546x^53+8418x^54+3948x^55+3564x^56+7566x^57+2556x^58+2076x^59+3974x^60+906x^61+504x^62+1120x^63+78x^64+136x^66+40x^69+14x^72

The gray image is a linear code over GF(3) with n=81, k=10 and d=39.
This code was found by Heurico 1.16 in 12.6 seconds.