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

generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+72x^81+136x^84+116x^87+572x^90+1044x^93+56x^96+46x^99+48x^102+32x^105+34x^108+14x^111+12x^114+2x^117+2x^135

The gray image is a linear code over GF(3) with n=138, k=7 and d=81.
This code was found by Heurico 1.16 in 0.101 seconds.