The generator matrix

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

generates a code of length 50 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+136x^44+820x^45+1691x^46+2990x^47+3386x^48+4718x^49+5180x^50+5066x^51+3688x^52+2732x^53+1192x^54+650x^55+276x^56+158x^57+40x^58+14x^59+16x^60+4x^61+9x^62+1x^64

The gray image is a code over GF(2) with n=400, k=15 and d=176.
This code was found by Heurico 1.16 in 7.55 seconds.