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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+60x^63+114x^66+142x^69+82x^72+5832x^74+68x^75+76x^78+54x^81+54x^84+34x^87+28x^90+14x^93+2x^111

The gray image is a linear code over GF(3) with n=333, k=8 and d=189.
This code was found by Heurico 1.16 in 0.197 seconds.