The generator matrix

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

generates a code of length 45 over Z3[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+144x^76+270x^77+540x^78+906x^79+984x^80+1220x^81+1824x^82+1920x^83+2388x^84+2958x^85+2556x^86+3488x^87+3912x^88+3234x^89+3950x^90+4476x^91+3486x^92+3884x^93+4188x^94+2958x^95+2770x^96+2442x^97+1590x^98+1160x^99+828x^100+408x^101+226x^102+162x^103+84x^104+42x^105+30x^106+6x^107+10x^108+4x^117

The gray image is a linear code over GF(3) with n=135, k=10 and d=76.
This code was found by Heurico 1.16 in 39.4 seconds.