The generator matrix

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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+46x^117+48x^118+186x^120+60x^121+1620x^122+66x^123+18x^124+70x^126+24x^127+28x^129+12x^130+6x^132+2x^183

The gray image is a linear code over GF(3) with n=549, k=7 and d=351.
This code was found by Heurico 1.16 in 0.12 seconds.