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

generates a code of length 51 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+64x^46+54x^47+131x^48+30x^49+261x^50+988x^51+278x^52+28x^53+72x^54+46x^55+68x^56+6x^57+18x^58+2x^60+1x^98

The gray image is a code over GF(2) with n=408, k=11 and d=184.
This code was found by Heurico 1.16 in 0.156 seconds.