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

generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+70x^105+144x^108+238x^111+282x^114+402x^117+470x^120+528x^123+506x^126+650x^129+698x^132+618x^135+588x^138+456x^141+368x^144+48x^146+216x^147+282x^149+240x^150+1200x^152+254x^153+3378x^155+334x^156+6402x^158+402x^159+9426x^161+524x^162+9462x^164+782x^165+6114x^167+850x^168+2658x^170+1078x^171+396x^173+1270x^174+1284x^177+1290x^180+1226x^183+1242x^186+856x^189+676x^192+486x^195+312x^198+180x^201+96x^204+44x^207+10x^210+6x^213+2x^216+2x^219+2x^222

The gray image is a linear code over GF(3) with n=243, k=10 and d=105.
This code was found by Heurico 1.16 in 99.6 seconds.