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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+60x^63+114x^66+142x^69+82x^72+1458x^74+68x^75+76x^78+54x^81+54x^84+34x^87+28x^90+14x^93+2x^111

The gray image is a linear code over GF(3) with n=111, k=7 and d=63.
This code was found by Heurico 1.16 in 0.0727 seconds.