The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  1  0  1  1  2  X  1  1 X+2  1  0  1  1  1  1  1  2  1  1  1  1 X+2  1  1  0  1  1  0  2  2  1  X  1  0  2  2  X  0  X
 0  1  1  0 X+1  1  X X+3  1 X+2  1  3  0 X+1  1  2 X+3  1  1 X+2  1  1  X  1  3  1 X+3 X+3  1  1  2  0  2  X  1  0 X+1  1  3  3  1  X  1  0  2 X+3  1  1  X  X  0  2
 0  0  X X+2  0 X+2  X X+2  X  0  2  0  2  0  0  X X+2 X+2  X  2  X  2 X+2  0  0  X X+2  X X+2 X+2 X+2  2  X X+2  2  2  2  2  0  0  0 X+2  0  0  X  0  0 X+2  X X+2  X  X
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  0  2  2  2  0  2  0  2  2  2  0  0  2  2  0  2  0  2  0  0  2  0  2  2  2  0  2  0  2  0  0  0  2  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  0  0  0  2  2  0  2  0  0  0  2  0  0  0  0  2  2  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  2  0  0  2  0  0  2  2  0  0  2  2  2  0  0  2  0  0  0  2  2  2  2  0  0  0  0  0  2  2  2  0  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  0  2  2  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2  0  2  2  0  2  2  2  2  2  0  2  2  2  2  0  0  0  0  2  0  0  0  2  0  2  0  0  0  2  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  2  2  0  2  2  2  0  2  2  0  2  0  2  2  0  0  2  0  2  0  0  0  0  2  0  0  0  2  2  2  0  0  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+67x^42+58x^43+285x^44+238x^45+716x^46+410x^47+1355x^48+618x^49+2337x^50+760x^51+2751x^52+696x^53+2365x^54+616x^55+1474x^56+416x^57+569x^58+190x^59+247x^60+74x^61+74x^62+14x^63+26x^64+6x^65+11x^66+5x^68+5x^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 10.9 seconds.