The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+36x^63+48x^65+132x^66+654x^68+252x^69+972x^70+2610x^71+1276x^72+5832x^73+5682x^74+4316x^75+11664x^76+7584x^77+4380x^78+7776x^79+4896x^80+268x^81+318x^83+158x^84+78x^86+42x^87+38x^90+20x^93+6x^96+10x^99

The gray image is a linear code over GF(3) with n=342, k=10 and d=189.
This code was found by Heurico 1.16 in 4.94 seconds.