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

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

Homogenous weight enumerator: w(x)=1x^0+130x^46+32x^47+94x^48+192x^49+324x^50+576x^51+256x^52+192x^53+120x^54+32x^55+31x^56+60x^58+6x^62+1x^64+1x^88

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 78.8 seconds.