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

generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+110x^54+304x^57+430x^60+774x^63+1706x^66+3638x^69+5174x^72+4292x^75+1918x^78+652x^81+366x^84+216x^87+64x^90+26x^93+8x^96+2x^99+2x^102

The gray image is a linear code over GF(3) with n=108, k=9 and d=54.
This code was found by Heurico 1.16 in 5.03 seconds.