The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+130x^69+12x^71+358x^72+60x^73+126x^74+558x^75+204x^76+324x^77+1290x^78+558x^79+876x^80+2882x^81+1524x^82+1860x^83+4948x^84+2544x^85+2628x^86+7034x^87+3078x^88+3054x^89+7082x^90+2694x^91+2472x^92+4726x^93+1788x^94+1260x^95+2412x^96+576x^97+432x^98+768x^99+96x^100+78x^101+328x^102+196x^105+58x^108+24x^111+8x^114+2x^117

The gray image is a linear code over GF(3) with n=132, k=10 and d=69.
This code was found by Heurico 1.16 in 32.4 seconds.