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

generates a code of length 76 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+70x^105+146x^108+228x^111+310x^114+344x^117+468x^120+514x^123+620x^126+658x^129+18x^131+658x^132+66x^134+654x^135+222x^137+768x^138+864x^140+748x^141+2352x^143+796x^144+4566x^146+748x^147+6834x^149+842x^150+8490x^152+976x^153+7806x^155+1090x^156+4998x^158+1206x^159+2376x^161+1274x^162+690x^164+1420x^165+84x^167+1286x^168+1206x^171+914x^174+642x^177+456x^180+292x^183+178x^186+82x^189+50x^192+26x^195+6x^198+6x^201

The gray image is a linear code over GF(3) with n=228, k=10 and d=105.
This code was found by Heurico 1.16 in 99.7 seconds.