The generator matrix

 1  0  0  0  0  1  1  1  0  1 2X  1 2X  1  1  1  1 2X  1  1  1 2X  X  1  0  0 2X  1  1  1  0  0  X  1  1  1  1 2X  1  1  1
 0  1  0  0  0 2X  1  1  1  X  0 2X+1  1 X+1 X+2 2X+2 2X+2  X  1 2X+1 2X+1 2X  1 X+2  1  1  1  2 2X 2X+2  1  1  0 2X+1  1 2X  2  1 2X+2  2  2
 0  0  1  0  0  0  0 2X 2X  X 2X 2X  0  0 2X 2X  X  1  1 X+1 2X+1  1 X+2 X+2 2X+2  2  2  2  1 2X+1 2X+2 2X  1  2 2X+1 X+1 X+2 2X+1  1 X+1 X+1
 0  0  0  1  0 2X+1  1 X+2  1 X+2  1  X  2 2X 2X  2 X+1  1 2X+2  0  1  2 2X+2 X+2 2X+1  2 2X 2X+1  0  2  0 2X+1 X+1 2X+2 X+2  1  X  2  X 2X+2  0
 0  0  0  0  1 2X+2  X 2X+2 X+2  1 2X+1 2X+1  1 X+2  0  1 X+2  2 2X+1 2X X+2 2X+1  0  X  X  2  2  0 2X+1  2 X+1 2X+1 X+1  X  0  X 2X+1 2X+1  2 X+2  1

generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+364x^69+252x^70+522x^71+1668x^72+948x^73+1014x^74+3296x^75+1446x^76+1788x^77+4838x^78+2268x^79+2496x^80+6774x^81+2736x^82+2952x^83+7138x^84+2874x^85+2502x^86+5392x^87+1788x^88+1302x^89+2522x^90+690x^91+462x^92+742x^93+108x^94+84x^95+42x^96+12x^97+22x^99+2x^102+2x^105+2x^117

The gray image is a linear code over GF(3) with n=123, k=10 and d=69.
This code was found by Heurico 1.16 in 39.6 seconds.