The generator matrix

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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+252x^61+408x^62+586x^63+1380x^64+1818x^65+1918x^66+3540x^67+4608x^68+3802x^69+7020x^70+8742x^71+7146x^72+11976x^73+13200x^74+10396x^75+15180x^76+15720x^77+11110x^78+13944x^79+12690x^80+7046x^81+8352x^82+6348x^83+2948x^84+3150x^85+1758x^86+796x^87+762x^88+300x^89+146x^90+54x^91+18x^92+16x^93+6x^96+6x^99+4x^102

The gray image is a linear code over GF(3) with n=114, k=11 and d=61.
This code was found by Heurico 1.16 in 253 seconds.