The generator matrix

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

generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+58x^45+150x^46+396x^47+850x^48+1008x^49+1470x^50+2870x^51+2964x^52+3996x^53+7432x^54+6786x^55+8424x^56+13968x^57+12126x^58+13386x^59+19656x^60+13866x^61+13410x^62+16374x^63+10326x^64+8226x^65+8490x^66+4308x^67+2694x^68+2142x^69+882x^70+468x^71+296x^72+72x^73+18x^74+20x^75+10x^78+4x^81

The gray image is a linear code over GF(3) with n=90, k=11 and d=45.
This code was found by Heurico 1.16 in 163 seconds.