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 X 1 X 1 1 1 X X 1 X 1 1 1 X X X X 1 1 1
0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 X^2 2X^2 2X^2 0 X^2 X^2 2X^2 2X^2 0 0 X^2 2X^2 0 X^2 2X^2 0 0 X^2 2X^2
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+72x^84+6x^93+2x^99
The gray image is a linear code over GF(3) with n=378, k=4 and d=252.
This code was found by Heurico 1.16 in 0.0164 seconds.