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

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+70x^69+114x^70+108x^71+464x^72+252x^73+736x^75+252x^76+56x^78+12x^79+54x^80+46x^81+18x^82+2x^84+2x^99

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 0.0303 seconds.