The generator matrix

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

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+150x^29+142x^30+636x^31+840x^32+962x^33+1908x^34+2442x^35+2480x^36+4446x^37+5886x^38+4570x^39+7062x^40+7044x^41+4718x^42+5652x^43+4470x^44+2096x^45+1980x^46+984x^47+328x^48+186x^49+54x^50+8x^51+4x^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 11.4 seconds.