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

generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+152x^69+422x^72+678x^75+6x^76+922x^78+96x^79+1166x^81+672x^82+1612x^84+2688x^85+1892x^87+6720x^88+2272x^90+10752x^91+2514x^93+10752x^94+2314x^96+6144x^97+1996x^99+1536x^100+1492x^102+1076x^105+630x^108+320x^111+118x^114+74x^117+24x^120+6x^123+2x^129

The gray image is a linear code over GF(3) with n=138, k=10 and d=69.
This code was found by Heurico 1.16 in 59.1 seconds.