The generator matrix

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

generates a code of length 19 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+134x^21+420x^24+794x^27+1454x^30+2598x^33+4374x^34+3594x^36+17496x^37+3822x^39+17496x^40+3210x^42+2088x^45+1066x^48+414x^51+84x^54+4x^57

The gray image is a linear code over GF(3) with n=57, k=10 and d=21.
This code was found by Heurico 1.16 in 6.68 seconds.