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  1  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 X^2 2X^2+2X X^2+X X^2+X  0 2X 2X^2+X X^2 X^2+2X X^2+X 2X^2 X^2+X 2X^2+X X^2 X^2+X 2X 2X^2+2X  0  X 2X^2+X 2X 2X^2 X^2  0
 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^2+X  X 2X^2 X^2+2X 2X 2X^2+2X  0 X^2+2X 2X^2+X  X  0 X^2 X^2+2X  X 2X^2+2X  0 2X^2 2X^2+X X^2+X 2X^2 2X 2X^2+X 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+72x^69+90x^70+72x^71+428x^72+204x^73+366x^74+602x^75+162x^76+24x^77+66x^78+18x^79+24x^80+30x^81+8x^84+6x^85+6x^87+6x^88+2x^102

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 0.0247 seconds.