The generator matrix
1 0 0 1 1 1 1 1 0 2X 1 1 1 1 1 2X 1 0 1 X 1 1 1 0 1 1 1 1 2X 1 1 1 1 1 2X 1 1 1 1 0 1 1 1 0 1 1 1 1 2X 0 1
0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 2X+1 1 1 1 1 2 1 X+2 X 0 0 2X+1 1 X 2 1 X+2 2 2X 1 1 1 2 2X+2 2X+1 2X+1 1 2X X 0 1 2X 1 2 X 1 1 0
0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 2X+2 1 X+1 2X 0 2X 2X+2 2X+1 2X+1 2X 1 X 2X+2 2X+2 2X 2X+2 X+2 X+2 2X X+1 X X+2 X+1 0 0 2 2X+1 2 1 2X X+2 2X 2X+1 2X+2 1 1 0 0
0 0 0 2X 0 0 0 0 0 0 0 0 0 2X X X X X X 2X 2X 2X X X 2X X 0 2X X X 0 2X 0 X X 2X 2X X X 0 2X 2X 0 2X 2X 0 2X X X 2X 0
0 0 0 0 2X 0 0 0 0 0 X 2X 2X 2X 2X X 2X 0 X X X 2X 0 0 2X X X X 2X 0 X 2X 0 2X 0 X 0 X 0 2X 0 2X 2X 2X 2X X 0 X 2X X 0
0 0 0 0 0 X 0 X X 2X 2X 2X 2X 2X 2X 0 2X 0 0 X 0 X 2X X 0 2X X 2X X 0 2X X 0 0 2X 0 0 0 X X 2X 2X 0 0 X X 0 0 X 0 0
0 0 0 0 0 0 X X X X X 2X X 2X 0 X X X X 2X X X X 0 X X 0 X X 2X 0 2X 2X 0 0 0 X 2X 0 2X X 0 X 0 0 2X 2X 2X 2X 0 0
generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+80x^84+30x^86+484x^87+150x^88+168x^89+1270x^90+534x^91+636x^92+2386x^93+966x^94+1140x^95+3526x^96+1698x^97+2100x^98+5080x^99+2538x^100+2814x^101+5964x^102+2748x^103+2814x^104+6094x^105+2400x^106+1956x^107+4352x^108+1458x^109+1140x^110+2344x^111+498x^112+282x^113+878x^114+126x^115+42x^116+212x^117+6x^118+74x^120+32x^123+20x^126+6x^129+2x^132
The gray image is a linear code over GF(3) with n=153, k=10 and d=84.
This code was found by Heurico 1.16 in 34.9 seconds.