The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+56x^75+6x^76+36x^77+202x^78+114x^79+150x^80+366x^81+330x^82+222x^83+450x^84+1236x^85+3138x^86+874x^87+2226x^88+6132x^89+850x^90+1668x^91+318x^92+484x^93+162x^94+174x^95+188x^96+90x^97+36x^98+90x^99+32x^102+28x^105+14x^108+4x^111+4x^114+2x^117

The gray image is a linear code over GF(3) with n=396, k=9 and d=225.
This code was found by Heurico 1.16 in 1.39 seconds.