The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+64x^27+168x^30+224x^33+790x^36+2304x^39+2330x^42+334x^45+222x^48+92x^51+26x^54+6x^57

The gray image is a linear code over GF(3) with n=60, k=8 and d=27.
This code was found by Heurico 1.16 in 0.23 seconds.