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

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+132x^117+162x^120+1458x^122+324x^123+82x^126+26x^135+2x^180

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 1.72 seconds.