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.