The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+60x^63+236x^66+446x^69+792x^72+978x^75+1358x^78+1670x^81+1458x^82+2054x^84+8748x^85+2336x^87+17496x^88+2366x^90+11664x^91+2240x^93+1988x^96+1422x^99+852x^102+472x^105+240x^108+112x^111+40x^114+10x^117+8x^120+2x^123

The gray image is a linear code over GF(3) with n=132, k=10 and d=63.
This code was found by Heurico 1.16 in 51.5 seconds.