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

generates a code of length 53 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+114x^81+284x^84+596x^87+810x^90+18x^92+1078x^93+252x^95+1310x^96+1512x^98+1708x^99+5040x^101+1946x^102+10080x^104+2060x^105+12096x^107+2166x^108+8064x^110+2218x^111+2304x^113+1838x^114+1396x^117+962x^120+610x^123+326x^126+142x^129+64x^132+38x^135+12x^138+2x^141+2x^144

The gray image is a linear code over GF(3) with n=159, k=10 and d=81.
This code was found by Heurico 1.16 in 71.6 seconds.