The generator matrix

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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+114x^40+210x^41+482x^42+1014x^43+1302x^44+2388x^45+3300x^46+4020x^47+5490x^48+8286x^49+8202x^50+11842x^51+15480x^52+13974x^53+16642x^54+18972x^55+14064x^56+14406x^57+13086x^58+8004x^59+6070x^60+4512x^61+2436x^62+1562x^63+786x^64+276x^65+138x^66+60x^67+20x^69+8x^72

The gray image is a linear code over GF(3) with n=81, k=11 and d=40.
This code was found by Heurico 1.16 in 143 seconds.