The generator matrix

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

generates a code of length 5 over Z3[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+30x^2+10x^3+360x^4+240x^5+2200x^6+2160x^7+7200x^8+8720x^9+12096x^10+13920x^11+8720x^12+2880x^13+480x^14+32x^15

The gray image is a linear code over GF(3) with n=15, k=10 and d=2.
This code was found by Heurico 1.16 in 0.14 seconds.