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

generates a code of length 48 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+196x^81+148x^84+18x^86+142x^87+180x^89+388x^90+720x^92+152x^93+1440x^95+13266x^96+1440x^98+346x^99+576x^101+124x^102+150x^105+238x^108+56x^111+50x^114+44x^117+4x^120+2x^126+2x^129

The gray image is a linear code over GF(3) with n=432, k=9 and d=243.
This code was found by Heurico 1.16 in 80.7 seconds.