The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+228x^28+324x^29+948x^30+1644x^31+1782x^32+3308x^33+5352x^34+6024x^35+9392x^36+13914x^37+14106x^38+17712x^39+21252x^40+17364x^41+18458x^42+16680x^43+10554x^44+7664x^45+5838x^46+2256x^47+1518x^48+702x^49+78x^50+32x^51+16x^54

The gray image is a linear code over GF(3) with n=60, k=11 and d=28.
This code was found by Heurico 1.16 in 104 seconds.