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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+130x^54+378x^57+580x^60+976x^63+54x^64+1284x^66+648x^67+1786x^69+3240x^70+2282x^72+8640x^73+2646x^75+12960x^76+2602x^78+10368x^79+2404x^81+3456x^82+1944x^84+1328x^87+710x^90+372x^93+176x^96+58x^99+18x^102+8x^105

The gray image is a linear code over GF(3) with n=114, k=10 and d=54.
This code was found by Heurico 1.16 in 41.7 seconds.