The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 2X X+3  1  1  0 X+3  6  1 2X+3  1  1  1  1  1  1  1 2X  1  1  1  1  X  1 2X  1 2X+6  1  1  1  1  1  1  1  1
 0  1  0  0  6 2X+4 2X+4  1 2X+2  8 X+8  1  1 2X+2 2X+5 2X+6  1  1 X+7  1 X+1 2X 2X 2X+8 X+3 2X+2 2X+7  1  3 2X  2  4  1  1  0 2X+4  1 X+8 2X+5 X+1  0 2X+7 2X+2  5 X+1
 0  0  1  1  2  2 2X+3  1 2X+2  X 2X+1 X+1 2X+2 X+5  0  1 X+4 X+3 X+6 2X+5  4 X+7 2X+3  4 X+8 X+7  8 2X 2X X+1 2X+6 2X+3 2X+1 X+5  1 X+7 2X+2  2  5 X+3 X+6 X+7 X+4 2X+1 2X
 0  0  0 2X  3  6  0 2X+6 X+3  X  3  0  3  3 2X+3 2X+3 2X+6 X+6 2X+6 X+6  3 X+3  X  X X+6 2X+6 2X+3 2X+3 X+3  0  0  6 X+3 X+3 X+6  X 2X+6 2X+3 X+3 X+6  6  6  0 2X+6  0

generates a code of length 45 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+950x^81+1044x^82+2340x^83+5808x^84+5652x^85+8784x^86+13320x^87+14598x^88+19134x^89+24954x^90+20718x^91+21042x^92+18522x^93+9414x^94+5310x^95+3648x^96+1062x^97+252x^98+402x^99+168x^102+24x^105

The gray image is a code over GF(3) with n=405, k=11 and d=243.
This code was found by Heurico 1.16 in 221 seconds.