The generator matrix

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

generates a code of length 86 over Z3[X]/(X^2) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+82x^147+170x^150+18x^151+18x^152+398x^153+66x^154+90x^155+778x^156+288x^157+414x^158+1246x^159+606x^160+510x^161+1922x^162+990x^163+1200x^164+3148x^165+1452x^166+1590x^167+4154x^168+1800x^169+2214x^170+5164x^171+2274x^172+2352x^173+5088x^174+1974x^175+1878x^176+4146x^177+1926x^178+1566x^179+3140x^180+984x^181+876x^182+1594x^183+498x^184+330x^185+812x^186+186x^187+66x^188+342x^189+60x^190+18x^191+272x^192+142x^195+122x^198+50x^201+22x^204+8x^207+4x^210

The gray image is a linear code over GF(3) with n=258, k=10 and d=147.
This code was found by Heurico 1.16 in 81.5 seconds.