The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  1  1  1  1  1  X  1  X  X  X  X  X  1  1  X  1  1  1  X  X  1  1  1  1  X  1  1  1  1
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2 X^2 X^2+2  0 X^2 X^2  0  2 X^2 X^2+2  0 X^2+2 X^2  0 X^2 X^2+2  2 X^2+2  2  2  0  0 X^2  2  2  0  0 X^2+2 X^2 X^2+2  2 X^2+2  0  2 X^2
 0  0 X^2+2 X^2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  0 X^2+2 X^2  0 X^2 X^2  0 X^2+2  2 X^2+2  0 X^2 X^2  0  2 X^2+2  2 X^2  0  2 X^2+2 X^2  2  0  0 X^2 X^2+2 X^2+2  2  2 X^2+2  2  0 X^2+2  0 X^2  0 X^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+6x^49+15x^50+210x^51+15x^52+6x^53+2x^67+1x^70

The gray image is a code over GF(2) with n=408, k=8 and d=196.
This code was found by Heurico 1.16 in 0.078 seconds.