The generator matrix

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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+160x^141+246x^142+390x^143+1186x^144+1644x^145+2370x^146+2498x^147+3540x^148+4146x^149+4100x^150+5202x^151+6324x^152+5348x^153+6114x^154+4842x^155+3514x^156+2976x^157+1998x^158+902x^159+558x^160+210x^161+254x^162+54x^163+90x^164+172x^165+54x^166+30x^167+58x^168+24x^169+6x^170+22x^171+6x^173+8x^174+2x^189

The gray image is a linear code over GF(3) with n=684, k=10 and d=423.
This code was found by Heurico 1.16 in 12.3 seconds.