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

generates a code of length 52 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+72x^78+238x^81+486x^84+768x^87+1076x^90+1412x^93+2944x^96+6906x^99+12176x^102+14316x^105+10284x^108+4222x^111+1530x^114+1072x^117+742x^120+422x^123+246x^126+70x^129+36x^132+22x^135+8x^138

The gray image is a linear code over GF(3) with n=156, k=10 and d=78.
This code was found by Heurico 1.16 in 68.8 seconds.