The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+64x^54+24x^56+194x^57+114x^59+334x^60+72x^61+336x^62+446x^63+450x^64+1140x^65+584x^66+1782x^67+2754x^68+652x^69+4500x^70+5196x^71+802x^72+7092x^73+6540x^74+826x^75+7290x^76+5580x^77+760x^78+4014x^79+3216x^80+706x^81+1044x^82+1206x^83+592x^84+138x^86+338x^87+160x^90+70x^93+20x^96+8x^99+2x^102+2x^105

The gray image is a linear code over GF(3) with n=111, k=10 and d=54.
This code was found by Heurico 1.16 in 23.4 seconds.