The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  1  1  1  1  0  1 2X^2+X  1  1 2X  1  1  1  1  1  1  1  1  1  1  X  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1  0  2 2X^2+X 2X^2+X+2 2X  1 2X^2+2X+1  1 2X^2+1 2X+2  1  0 2X X^2 2X^2+X 2X^2+2X+1 2X^2+1 2X^2+X+2 X^2+X+2 X^2+2X X^2+X X^2+X X^2+X+1 X+2
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2  0 X^2 2X^2  0  0 X^2 X^2 2X^2  0 X^2 2X^2  0 2X^2  0 2X^2
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2 X^2 X^2  0 2X^2  0  0 X^2 X^2  0 2X^2 X^2  0 X^2 2X^2  0  0 X^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+558x^69+414x^70+968x^72+1188x^73+1336x^75+1242x^76+702x^78+72x^79+64x^81+12x^84+2x^90+2x^102

The gray image is a linear code over GF(3) with n=333, k=8 and d=207.
This code was found by Heurico 1.16 in 3.84 seconds.