The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+156x^29+270x^30+288x^31+1188x^32+1164x^33+1020x^34+3072x^35+3000x^36+2784x^37+6774x^38+6132x^39+4494x^40+8220x^41+6036x^42+3408x^43+5352x^44+2628x^45+1104x^46+1440x^47+402x^48+24x^49+42x^50+36x^51+14x^54

The gray image is a linear code over GF(3) with n=60, k=10 and d=29.
This code was found by Heurico 1.16 in 8.46 seconds.