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

generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+228x^138+474x^139+594x^140+968x^141+1224x^142+1218x^143+1506x^144+1932x^145+1662x^146+2104x^147+2472x^148+2202x^149+2426x^150+3042x^151+2688x^152+2838x^153+3348x^154+2556x^155+3020x^156+3288x^157+2400x^158+2700x^159+2646x^160+2070x^161+2074x^162+1938x^163+1200x^164+1156x^165+1002x^166+630x^167+504x^168+396x^169+234x^170+124x^171+90x^172+36x^173+26x^174+18x^175+6x^176+8x^177

The gray image is a linear code over GF(3) with n=231, k=10 and d=138.
This code was found by Heurico 1.16 in 72.7 seconds.