The generator matrix

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

generates a code of length 48 over Z3[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+162x^86+250x^87+252x^88+1272x^89+1266x^90+1656x^91+3354x^92+4220x^93+5058x^94+7062x^95+7624x^96+7362x^97+7344x^98+5376x^99+3042x^100+1992x^101+768x^102+126x^103+444x^104+128x^105+186x^107+24x^108+54x^110+16x^111+8x^114+2x^117

The gray image is a linear code over GF(3) with n=432, k=10 and d=258.
This code was found by Heurico 1.16 in 6.93 seconds.