The generator matrix

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

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+90x^49+168x^50+106x^51+37x^52+38x^53+46x^54+14x^55+1x^56+8x^57+1x^58+1x^60+1x^74

The gray image is a code over GF(2) with n=408, k=9 and d=196.
This code was found by Heurico 1.16 in 0.109 seconds.