The generator matrix

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

generates a code of length 39 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+66x^54+242x^57+486x^60+764x^63+18x^64+1110x^66+252x^67+1406x^69+1512x^70+1850x^72+5040x^73+2338x^75+10080x^76+2538x^78+12096x^79+2568x^81+8064x^82+2254x^84+2304x^85+1686x^87+1180x^90+648x^93+346x^96+124x^99+50x^102+18x^105+8x^108

The gray image is a linear code over GF(3) with n=117, k=10 and d=54.
This code was found by Heurico 1.16 in 41.5 seconds.