The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+24x^73+36x^74+12x^76+4x^78+2x^84+2x^93

The gray image is a linear code over GF(3) with n=111, k=4 and d=73.
This code was found by Heurico 1.16 in 0.00347 seconds.