The generator matrix

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

generates a code of length 25 over Z3[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+186x^44+190x^45+294x^47+206x^48+4902x^50+94x^51+246x^53+142x^54+192x^56+80x^57+12x^59+14x^60+2x^75

The gray image is a linear code over GF(3) with n=225, k=8 and d=132.
This code was found by Heurico 1.16 in 0.0767 seconds.