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

generates a code of length 76 over Z3[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+360x^136+504x^137+216x^138+1122x^139+1482x^140+450x^141+1998x^142+2292x^143+704x^144+2760x^145+3102x^146+798x^147+3354x^148+3486x^149+922x^150+3942x^151+4062x^152+946x^153+4038x^154+4122x^155+924x^156+3618x^157+3132x^158+804x^159+2754x^160+2298x^161+480x^162+1404x^163+1236x^164+230x^165+666x^166+396x^167+54x^168+180x^169+114x^170+20x^171+42x^172+18x^173+8x^174+6x^175+2x^177+2x^183

The gray image is a linear code over GF(3) with n=228, k=10 and d=136.
This code was found by Heurico 1.16 in 80.2 seconds.