The generator matrix

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

generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+158x^168+288x^171+48x^172+102x^173+642x^174+162x^175+294x^176+914x^177+372x^178+372x^179+1644x^180+714x^181+906x^182+2328x^183+1134x^184+1242x^185+3252x^186+1506x^187+1680x^188+4520x^189+2046x^190+2172x^191+5016x^192+2154x^193+2124x^194+4622x^195+2136x^196+1806x^197+3818x^198+1404x^199+1242x^200+2456x^201+876x^202+696x^203+1474x^204+360x^205+354x^206+680x^207+162x^208+114x^209+364x^210+48x^211+18x^212+250x^213+148x^216+88x^219+72x^222+50x^225+14x^228+4x^231+2x^234

The gray image is a linear code over GF(3) with n=288, k=10 and d=168.
This code was found by Heurico 1.16 in 93.7 seconds.