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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+84x^57+262x^60+380x^63+480x^66+162x^68+602x^69+1296x^71+716x^72+3888x^74+790x^75+5184x^77+826x^78+2592x^80+852x^81+664x^84+426x^87+278x^90+136x^93+44x^96+14x^99+6x^102

The gray image is a linear code over GF(3) with n=114, k=9 and d=57.
This code was found by Heurico 1.16 in 5.34 seconds.