The generator matrix

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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+46x^138+54x^139+78x^140+268x^141+348x^142+762x^143+774x^144+1086x^145+2442x^146+1336x^147+2892x^148+5892x^149+3074x^150+5784x^151+8388x^152+3542x^153+5532x^154+7332x^155+2260x^156+2712x^157+2484x^158+708x^159+510x^160+246x^161+208x^162+24x^163+54x^164+70x^165+12x^166+24x^167+36x^168+34x^171+6x^174+14x^177+2x^180+6x^183+4x^186+2x^189+2x^192

The gray image is a linear code over GF(3) with n=684, k=10 and d=414.
This code was found by Heurico 1.16 in 12 seconds.