The generator matrix

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

generates a code of length 31 over Z3[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+236x^48+522x^49+456x^50+1310x^51+2304x^52+1698x^53+3706x^54+6150x^55+3978x^56+7786x^57+12390x^58+7872x^59+12688x^60+20082x^61+10062x^62+15330x^63+20094x^64+9408x^65+11580x^66+12438x^67+4518x^68+4890x^69+4074x^70+1200x^71+1344x^72+648x^73+168x^74+160x^75+30x^76+6x^77+10x^78+4x^81+2x^84+2x^87

The gray image is a linear code over GF(3) with n=93, k=11 and d=48.
This code was found by Heurico 1.16 in 177 seconds.