The generator matrix

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

generates a code of length 61 over Z3[X]/(X^2) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+162x^106+156x^107+392x^108+828x^109+540x^110+1100x^111+1650x^112+1008x^113+1942x^114+2760x^115+1458x^116+2436x^117+3750x^118+2028x^119+3188x^120+4404x^121+2376x^122+3510x^123+4542x^124+2262x^125+3216x^126+3930x^127+1752x^128+2188x^129+2658x^130+1092x^131+1034x^132+1176x^133+390x^134+478x^135+294x^136+54x^137+134x^138+90x^139+6x^140+28x^141+16x^144+14x^147+2x^150+4x^153

The gray image is a linear code over GF(3) with n=183, k=10 and d=106.
This code was found by Heurico 1.16 in 45.4 seconds.