The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+94x^66+72x^67+72x^68+238x^69+96x^70+72x^71+246x^72+90x^73+162x^74+284x^75+102x^76+144x^77+202x^78+84x^79+36x^80+90x^81+36x^82+30x^84+6x^85+8x^87+14x^90+6x^93+2x^96

The gray image is a linear code over GF(3) with n=111, k=7 and d=66.
This code was found by Heurico 1.16 in 0.046 seconds.