The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+72x^51+304x^54+586x^57+864x^60+1386x^63+3086x^66+7132x^69+12524x^72+14724x^75+10666x^78+4492x^81+1460x^84+924x^87+450x^90+220x^93+104x^96+40x^99+12x^102+2x^105

The gray image is a linear code over GF(3) with n=111, k=10 and d=51.
This code was found by Heurico 1.16 in 38.2 seconds.