The generator matrix

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

generates a code of length 8 over Z3[X]/(X^3) who�s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+90x^10+264x^11+850x^12+540x^13+7902x^14+3336x^15+25866x^16+15804x^17+3332x^18+720x^19+330x^20+8x^21+6x^24

The gray image is a linear code over GF(3) with n=72, k=10 and d=30.
This code was found by Heurico 1.16 in 0.363 seconds.