The generator matrix

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

generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+252x^8+130x^9+2592x^10+1512x^11+22512x^12+10368x^13+82242x^14+44982x^15+10368x^16+2016x^17+166x^18+6x^21

The gray image is a linear code over GF(3) with n=63, k=11 and d=24.
This code was found by Heurico 1.16 in 1.45 seconds.