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 X 1 1 X 1 1 X 1 X 1 1 1 1 1 1 X 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 X X 2X 2X 2X X 2X X X X X X 2X X X 0 X 0 X 2X 2X 0 2X 2X 0 X 2X 0
0 0 X 0 0 0 0 0 0 0 0 X X 2X X 0 X 2X 2X 2X 0 0 X 2X X X 0 2X X 0 X 0 2X 2X X 2X X X 2X 2X 0
0 0 0 X 0 0 0 0 X 2X 2X 2X 2X 2X X 0 X 2X 0 0 0 2X 2X X 2X 0 X X 2X X X X 0 2X X 2X X 2X X 2X 0
0 0 0 0 X 0 0 X 2X 0 2X 2X X X X 2X X X 0 2X X 2X 2X X X X 2X X X 2X 0 0 X 2X 2X X X 2X X 2X 2X
0 0 0 0 0 X 0 2X 2X X 0 2X 2X X 2X 2X X 2X 2X X 2X X 2X X X 0 X 0 2X 2X 2X 0 2X 0 0 2X X 0 0 2X X
0 0 0 0 0 0 X 2X 2X 2X 2X X 0 X X 0 0 X 2X X X X X 0 2X 2X 0 X X 0 0 0 2X 0 0 2X X 0 2X 0 2X
generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.
Homogenous weight enumerator: w(x)=1x^0+64x^66+146x^69+268x^72+410x^75+948x^78+1672x^81+1678x^84+790x^87+226x^90+162x^93+104x^96+72x^99+8x^102+10x^105+2x^108
The gray image is a linear code over GF(3) with n=123, k=8 and d=66.
This code was found by Heurico 1.16 in 0.698 seconds.