The generator matrix

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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+720x^142+1230x^143+4514x^144+7104x^145+9324x^146+14212x^147+18444x^148+22332x^149+28462x^150+37938x^151+39882x^152+44942x^153+52332x^154+49002x^155+47182x^156+45756x^157+35154x^158+28306x^159+20202x^160+10848x^161+7252x^162+3792x^163+1242x^164+682x^165+234x^166+96x^167+70x^168+72x^169+6x^170+54x^171+24x^172+12x^173+6x^174+6x^175+6x^177

The gray image is a linear code over GF(3) with n=693, k=12 and d=426.
This code was found by Heurico 1.16 in 629 seconds.