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 X 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 2X X 0 0 X X 0 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 0 2X 0 0 X X 0 0 2X
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 X 2X 2X 2X 0 0 0 0 2X
generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.
Homogenous weight enumerator: w(x)=1x^0+20x^81+78x^84+124x^87+8x^90+8x^96+2x^99+2x^126
The gray image is a linear code over GF(3) with n=129, k=5 and d=81.
This code was found by Heurico 1.16 in 0.00763 seconds.