The generator matrix

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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+344x^81+594x^82+360x^84+324x^85+336x^87+216x^88+6x^90+6x^96

The gray image is a linear code over GF(3) with n=378, k=7 and d=243.
This code was found by Heurico 1.16 in 0.027 seconds.