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

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+250x^69+438x^70+594x^71+1218x^72+1230x^73+1440x^74+2360x^75+1998x^76+2340x^77+3784x^78+2982x^79+3426x^80+4610x^81+3582x^82+3936x^83+5336x^84+3594x^85+3360x^86+4212x^87+2490x^88+1692x^89+1788x^90+912x^91+618x^92+436x^93+240x^94+78x^95+50x^96+30x^97+12x^98+6x^99+2x^102+2x^105+2x^111

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 30.7 seconds.