The generator matrix

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

generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+40x^78+164x^81+550x^84+1158x^87+2140x^90+3386x^93+4242x^96+4030x^99+2386x^102+1080x^105+304x^108+96x^111+64x^114+30x^117+8x^120+4x^123

The gray image is a linear code over GF(3) with n=144, k=9 and d=78.
This code was found by Heurico 1.16 in 4.49 seconds.