The generator matrix

 1  0  1  1  1  0  1  1  2  1  0  1  1  1  X  1  X  1  1 X+2  1  1  0  1  1  X  1  1  X  0  1  2  1  1  1  1  0  1  0  0  1  1  1  1  X  1  2  2  X  X X+2  1
 0  1  1  0 X+1  1  0 X+1  1  2  1  1  0 X+3  1 X+2  1  3  X  1  3 X+2  1  X X+3  1  2 X+3  1  1  X  1 X+1 X+3  0  2  1  0  1  2  1 X+2  2 X+3  1  3  0  1  0  1  1  0
 0  0  X  0  X  0  X  0  X X+2  X  0  2  X X+2  X  0  2  X  0  X  0  X  2  2 X+2  X  2 X+2  2  2 X+2  X  0 X+2  0  0  0 X+2  0  X  X X+2 X+2  0  X  X  2  0  2  X  0
 0  0  0  X  X X+2  X  0  0  2 X+2 X+2 X+2  2  2 X+2  X  0  0  2  X  0  X  X  X  X  2 X+2  2  2  0  0 X+2 X+2  X  X  X  2  X  X  X X+2  X X+2 X+2  X X+2  2 X+2 X+2  X  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  0  2  2  2  0  0  2  2  0  0  0  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0  2  2  2  2  2  2  0  0  2  0
 0  0  0  0  0  2  0  0  2  2  0  0  2  0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  0  0  2  0  0  0  2  0  2  2  0  0  0  2  2  2  0
 0  0  0  0  0  0  2  0  2  2  2  2  0  2  0  0  2  0  2  0  0  2  0  0  2  2  0  0  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  0  2  0  0  0  0  2  2  0  2  2  2  2  0  2  0  0  2  0  0  0  2  2  2  0  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+56x^42+82x^43+213x^44+334x^45+509x^46+664x^47+983x^48+1246x^49+1484x^50+1760x^51+1717x^52+1826x^53+1591x^54+1266x^55+866x^56+594x^57+464x^58+292x^59+171x^60+88x^61+107x^62+30x^63+14x^64+8x^65+12x^66+2x^67+3x^68+1x^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 11.3 seconds.