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  1  X  1  X  1  1  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0 2X  X 2X 2X 2X  X  X  X 2X  X 2X  X  X  0  X  0 2X  X 2X  X  X 2X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X 2X 2X  X 2X  0  X 2X 2X  0  X  0 2X  X 2X  X  X 2X 2X 2X  0  0  0  0
 0  0  0  X  0  0  0  0  0  X  X 2X  X 2X  X 2X 2X 2X  X 2X  0  0  X  0 2X  0 2X  0  0 2X 2X 2X  X  0  X  X  0
 0  0  0  0  X  0  0  0  X 2X 2X 2X  X  X 2X 2X 2X  X  0 2X  X  0  0  X  X 2X  0  X  0 2X  0  0 2X 2X 2X 2X  0
 0  0  0  0  0  X  0  0 2X 2X  X  X  X  0  X  X  0  0 2X 2X  X 2X  X  X  X 2X 2X  0  X  0 2X  0  0 2X  X  0  0
 0  0  0  0  0  0  X  0 2X  X 2X  X  0 2X  0 2X 2X 2X  0  0  X  X  X 2X  0  X  X  X  0  X 2X  X 2X  X  0  X  0
 0  0  0  0  0  0  0  X  X  0  X  0 2X  X  0 2X 2X  0  X 2X 2X  X  0  X  0  0  X  X  X  0  X 2X  X 2X  X 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+62x^54+186x^57+342x^60+488x^63+536x^66+486x^68+650x^69+2916x^71+798x^72+5832x^74+806x^75+3888x^77+820x^78+718x^81+556x^84+316x^87+170x^90+74x^93+32x^96+4x^99+2x^102

The gray image is a linear code over GF(3) with n=111, k=9 and d=54.
This code was found by Heurico 1.16 in 4.88 seconds.