The generator matrix

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

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+44x^18+54x^20+190x^21+54x^22+432x^23+732x^24+540x^25+1404x^26+3410x^27+2160x^28+2592x^29+9180x^30+4320x^31+3456x^32+12018x^33+4320x^34+3456x^35+6426x^36+1728x^37+1728x^38+618x^39+156x^42+28x^45+2x^48

The gray image is a linear code over GF(3) with n=48, k=10 and d=18.
This code was found by Heurico 1.16 in 2.98 seconds.