The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 X 1 1 1 1 X 2X 1 X 0 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 0 2 1 X X+1 1 2 2X+1 0 2 2X+1 1 X+2 2X+1 X+2 1 1 1 0 2X 1 X+2 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X X 2X X 2X X X 2X 2X X X 2X X 0 X X X X 2X 0 0
0 0 0 X 0 0 0 0 X 2X X 2X X 2X 2X 0 0 0 0 2X X 2X X 2X 0 X X 2X X X X X X X 0 2X 0
0 0 0 0 X 0 0 X 2X 2X X X 0 2X 2X 2X 2X X X 2X 2X 0 X X 0 2X 0 X 0 X 2X X 2X X 0 X 0
0 0 0 0 0 2X 0 2X X 0 X X 2X 2X X 2X 0 0 2X 0 X X 0 X 0 0 X 0 0 2X X X 2X 2X 0 0 0
0 0 0 0 0 0 X 2X 0 2X 2X X X 2X 2X X 2X 0 0 X 0 0 0 2X X X 0 0 X X 2X 0 2X X 2X X 0
generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.
Homogenous weight enumerator: w(x)=1x^0+44x^57+162x^60+598x^63+1274x^66+2430x^69+4268x^72+4692x^75+3662x^78+1828x^81+498x^84+110x^87+82x^90+24x^93+8x^96+2x^102
The gray image is a linear code over GF(3) with n=111, k=9 and d=57.
This code was found by Heurico 1.16 in 3.04 seconds.