The generator matrix

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

generates a code of length 48 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+59x^44+266x^45+171x^46+412x^47+243x^48+400x^49+168x^50+260x^51+56x^52+6x^53+3x^54+2x^58+1x^76

The gray image is a code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 0.109 seconds.