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  X  0  2  X  X  0  X  1  0  2  X  0  2  1  1  1  1  X  1  X  1  1  1  2  1  1  X
 0  X  0  X  0  0  X X+2  0  2  X  0 X+2  2 X+2 X+2  0  2  X  2  X  0 X+2 X+2  X  X  X  X X+2 X+2  X  X  X  X  X X+2  0  0  0 X+2  X  X X+2  0  X  X  2  2  X  0  2  X
 0  0  X  X  0 X+2  X  0  0  X  X  2  2 X+2  X  0  2  X  X X+2  0  0  2  X  0  X  2  X  2  2  2 X+2  X  2  X  2  X  X  2  2  0 X+2  2  X X+2  2  X  X X+2  0  0  X
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  0  2  0  0  0  2  0  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  2  0  0  0  2  2  0  2  0  2  2  0  2  2  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  0  0  0  2  0  0  0  0  2  0  2  2  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  0  2  0  0  2  2  0  0  2  2  0  2  2  0  2  2  2
 0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  0  2  0  0  0  2  0  0  2  0  0  2  2  2  0  2
 0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  0  0  0  2  2  0  0  2  2  2  2  0  2  0  2  2  0  0  0  2  0  0  2  2  2  2  0  2  2  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+78x^42+276x^44+16x^45+478x^46+112x^47+712x^48+336x^49+971x^50+560x^51+1143x^52+560x^53+1036x^54+336x^55+658x^56+112x^57+420x^58+16x^59+234x^60+70x^62+43x^64+11x^66+3x^68+8x^70+2x^72

The gray image is a code over GF(2) with n=208, k=13 and d=84.
This code was found by Heurico 1.16 in 4.38 seconds.