The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  X  1  1 X^2+2  1  1  2  1  1 X^2+X  1  1 X^2  1  1 X+2  1  1  X  1  1  1  1  1  1 X^2  1  1  1  1 X+2  1  1  0  1  1  1  1  1  1  1 X^2+X+2  1
 0  1 X+1 X^2+X+2 X^2+1  1  X X^2+X+1  1 X^2+2  3  1  2 X+1  1 X^2+X X^2+3  1 X+2 X^2+X+3  1 X^2  1  1  0 X^2+X+2 X^2+2 X+2 X^2  0 X^2+X X+3 X^2+X+1  1 X^2+2 X+2  2 X+2  1 X^2+3  3  0  X X+3 X^2  1 X^2+X+2  2 X^2+X  1  2
 0  0 X^2 X^2+2  2 X^2 X^2 X^2+2 X^2+2  2  0  2 X^2  0 X^2  0 X^2  0  2  2 X^2+2 X^2+2 X^2+2  2  2 X^2 X^2 X^2+2  0 X^2+2  2  2 X^2 X^2 X^2  0  0 X^2  0 X^2+2  2 X^2 X^2+2  0  2  0  2 X^2+2  0 X^2+2 X^2

generates a code of length 51 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+308x^49+158x^50+260x^51+61x^52+104x^53+33x^54+84x^55+1x^56+12x^57+1x^70+1x^76

The gray image is a code over GF(2) with n=408, k=10 and d=196.
This code was found by Heurico 1.16 in 105 seconds.