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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+204x^126+216x^129+1458x^130+216x^132+72x^135+18x^144+2x^189

The gray image is a linear code over GF(3) with n=585, k=7 and d=378.
This code was found by Heurico 1.16 in 0.354 seconds.