The generator matrix

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

generates a code of length 19 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+112x^27+114x^28+606x^29+856x^30+630x^31+2172x^32+2178x^33+2088x^34+5772x^35+5102x^36+4182x^37+8250x^38+6610x^39+4338x^40+7008x^41+3804x^42+1584x^43+2382x^44+962x^45+186x^46+54x^47+40x^48+12x^51+6x^54

The gray image is a linear code over GF(3) with n=57, k=10 and d=27.
This code was found by Heurico 1.16 in 7.64 seconds.