The generator matrix

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

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+26x^42+108x^43+196x^44+316x^45+466x^46+718x^47+934x^48+1230x^49+1621x^50+1712x^51+1741x^52+1704x^53+1637x^54+1384x^55+914x^56+612x^57+406x^58+272x^59+156x^60+92x^61+62x^62+26x^63+23x^64+14x^65+3x^66+4x^67+3x^68+3x^70

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 11.4 seconds.