The generator matrix

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

generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+94x^174+234x^175+432x^176+740x^177+804x^178+924x^179+1670x^180+1308x^181+1398x^182+2146x^183+1866x^184+1980x^185+2620x^186+1974x^187+2196x^188+3114x^189+2142x^190+2166x^191+3366x^192+2370x^193+2256x^194+3184x^195+2202x^196+2286x^197+2502x^198+1686x^199+1692x^200+2318x^201+1470x^202+1188x^203+1304x^204+876x^205+618x^206+648x^207+414x^208+252x^209+284x^210+108x^211+84x^212+36x^213+30x^214+24x^215+28x^216+12x^217+2x^225

The gray image is a linear code over GF(3) with n=288, k=10 and d=174.
This code was found by Heurico 1.16 in 95.2 seconds.