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 X 1 1 1 1 1 1 1
0 X 0 0 0 0 X 2X 2X 0 0 X X X X X X X 0 2X 0 2X 0 2X 0 X X 2X X 0 X 0 2X 2X X 0 2X X 0 X 0 X
0 0 X 0 0 X 2X 0 2X 0 X X 2X 2X 0 X 0 X X X X 0 0 2X 2X X 2X 0 X 2X 2X 0 0 2X 0 2X 0 X 2X 2X 2X 0
0 0 0 X 0 2X 2X X 0 X X 0 0 X 2X X X 2X 2X 0 0 2X 2X 2X 2X 2X 0 0 X X X X 0 2X 0 X 2X 2X 0 2X 0 0
0 0 0 0 X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 X 0 0 2X 2X X 2X X 2X 2X 0 0 0 X X X X X X X 0 0 X X X
generates a code of length 42 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.
Homogenous weight enumerator: w(x)=1x^0+82x^78+58x^81+162x^82+324x^85+58x^87+8x^90+20x^96+14x^99+2x^123
The gray image is a linear code over GF(3) with n=126, k=6 and d=78.
This code was found by Heurico 1.16 in 0.0166 seconds.