The generator matrix

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

generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+106x^72+72x^73+162x^74+480x^75+228x^76+252x^77+646x^78+294x^79+324x^80+796x^81+300x^82+216x^83+680x^84+282x^85+234x^86+496x^87+174x^88+216x^89+306x^90+96x^91+54x^92+114x^93+12x^94+8x^96+6x^99+4x^102+2x^105

The gray image is a linear code over GF(3) with n=123, k=8 and d=72.
This code was found by Heurico 1.16 in 0.342 seconds.