The generator matrix

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

generates a code of length 62 over Z3[X]/(X^2) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+146x^114+216x^115+258x^116+448x^117+360x^118+456x^119+488x^120+330x^121+294x^122+444x^123+306x^124+258x^125+360x^126+246x^127+324x^128+284x^129+174x^130+162x^131+322x^132+186x^133+120x^134+76x^135+96x^136+48x^137+80x^138+18x^139+12x^140+12x^141+12x^142+12x^143+12x^144

The gray image is a linear code over GF(3) with n=186, k=8 and d=114.
This code was found by Heurico 1.16 in 0.641 seconds.