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

generates a code of length 42 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+52x^81+162x^84+26x^90+2x^126

The gray image is a linear code over GF(3) with n=126, k=5 and d=81.
This code was found by Heurico 1.16 in 0.0154 seconds.