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
 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  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  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  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  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  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  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  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

generates a code of length 77 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+710x^132+696x^135+852x^138+1424x^141+2524x^144+4410x^147+6898x^150+8540x^153+8374x^156+7060x^159+4774x^162+2590x^165+1760x^168+1320x^171+1050x^174+980x^177+708x^180+448x^183+304x^186+160x^189+94x^192+40x^195+28x^198+6x^204

The gray image is a linear code over GF(3) with n=231, k=10 and d=105.
This code was found by Heurico 1.16 in 99.7 seconds.