The generator matrix

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

generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+136x^141+24x^142+66x^143+352x^144+168x^145+186x^146+446x^147+168x^148+174x^149+510x^150+264x^151+222x^152+520x^153+234x^154+252x^155+566x^156+216x^157+258x^158+432x^159+240x^160+252x^161+360x^162+84x^163+48x^164+158x^165+48x^166+52x^168+12x^169+40x^171+28x^174+16x^177+12x^180+4x^183+4x^186+4x^192+2x^195+2x^198

The gray image is a linear code over GF(3) with n=231, k=8 and d=141.
This code was found by Heurico 1.16 in 0.981 seconds.