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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+234x^74+102x^75+162x^76+342x^77+540x^78+324x^79+306x^80+60x^81+36x^83+24x^84+36x^86+18x^89+2x^108

The gray image is a linear code over GF(3) with n=351, k=7 and d=222.
This code was found by Heurico 1.16 in 0.499 seconds.