The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 1 1 1 0 2X 1 1 1 1 1 1 0 0 1 1 1 1 X 0 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 2 1 1 X+2 0 2X+1 0 X+2 2X+1 0 2 1 1 X+1 2 X 2X+1 2 2X+2 1 1 2X+1 X 2X X+1 X 1 2
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X 2X 2X 0 2X X X 0 2X X X 2X X 2X 2X 2X 0 X X 0 0 2X X 0 2X 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X X 2X 0 X X X 0 2X X 2X X 0 X X 0 2X 2X 0 X X X 2X 2X 2X X 2X
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X X 2X X X 0 2X X X X 2X 0 X X X 0 2X 0 2X 0 2X 2X X 2X 0 0 X 2X X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X X X 0 X 2X X 2X X 0 2X 2X 0 X X 2X 2X 2X 0 2X X X 0 X X 2X X 2X 2X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X 0 X 2X 0 0 X 0 X 2X X X 0 X 0 2X X 2X 0 X X 2X 0 2X 2X X 0 2X X
generates a code of length 42 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.
Homogenous weight enumerator: w(x)=1x^0+144x^69+108x^71+256x^72+402x^74+412x^75+1170x^77+728x^78+2142x^80+1036x^81+3030x^83+1314x^84+3132x^86+1164x^87+2178x^89+796x^90+834x^92+380x^93+126x^95+162x^96+90x^99+52x^102+16x^105+8x^108+2x^111
The gray image is a linear code over GF(3) with n=126, k=9 and d=69.
This code was found by Heurico 1.16 in 4.11 seconds.