The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+384x^48+192x^49+384x^50+160x^51+449x^52+128x^53+256x^54+32x^55+55x^56+2x^60+4x^64+1x^76

The gray image is a code over GF(2) with n=408, k=11 and d=192.
This code was found by Heurico 1.16 in 0.563 seconds.