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

generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+68x^105+132x^108+244x^111+310x^114+382x^117+450x^120+528x^123+580x^126+604x^129+704x^132+6x^134+630x^135+66x^137+526x^138+264x^140+544x^141+732x^143+566x^144+1884x^146+524x^147+3756x^149+576x^150+6222x^152+612x^153+7770x^155+710x^156+7464x^158+886x^159+5964x^161+1090x^162+3546x^164+1224x^165+1314x^167+1272x^168+360x^170+1400x^171+18x^173+1302x^174+1050x^177+980x^180+708x^183+448x^186+304x^189+160x^192+94x^195+40x^198+28x^201+6x^207

The gray image is a linear code over GF(3) with n=234, k=10 and d=105.
This code was found by Heurico 1.16 in 99.3 seconds.