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

generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+212x^42+534x^44+8x^45+788x^46+72x^47+1077x^48+632x^49+2153x^50+1336x^51+2794x^52+1336x^53+2088x^54+632x^55+1221x^56+72x^57+718x^58+8x^59+434x^60+172x^62+76x^64+13x^66+6x^68+1x^88

The gray image is a code over GF(2) with n=208, k=14 and d=84.
This code was found by Heurico 1.16 in 19.4 seconds.