The generator matrix

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

generates a code of length 52 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+146x^84+12x^86+302x^87+18x^88+96x^89+652x^90+126x^91+312x^92+1152x^93+342x^94+756x^95+2358x^96+1026x^97+1488x^98+4320x^99+2394x^100+2400x^101+5690x^102+3042x^103+2700x^104+7020x^105+3024x^106+2550x^107+5568x^108+2178x^109+1806x^110+3128x^111+828x^112+744x^113+1394x^114+144x^115+240x^116+552x^117+18x^119+280x^120+148x^123+58x^126+26x^129+10x^132

The gray image is a linear code over GF(3) with n=156, k=10 and d=84.
This code was found by Heurico 1.16 in 54.7 seconds.