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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+106x^69+54x^70+62x^72+216x^73+1458x^74+216x^76+26x^78+10x^81+28x^87+8x^90+2x^105

The gray image is a linear code over GF(3) with n=333, k=7 and d=207.
This code was found by Heurico 1.16 in 88.4 seconds.