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 X X X X 0 X^2 X X 2X^2 1 1 1 1 1 1
0 X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X 0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2 X 2X^2+2X 0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2 X 2X^2+2X 2X^2+X 2X X^2+X X^2+2X X X X 2X^2+2X X 0 X^2 2X^2 2X^2+X X^2+X X
generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+234x^84+4x^90+4x^99
The gray image is a linear code over GF(3) with n=378, k=5 and d=252.
This code was found by Heurico 1.16 in 0.0167 seconds.