The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  1  1  1  1  X  0  1  1  1  X  1  1  1  1  0  1  1  1  0  1  1  1  1  X  X  X  1  1
 0  X  0 X+2  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  X  0  2  0  0  2 X+2  X X+2  X X+2 X+2  X X+2 X+2  X  0 X+2  2 X+2  0  X  2  0  X  0  0 X+2  X  X X+2  X X+2 X+2 X+2 X+2  2  0
 0  0  2  0  0  0  0  0  0  0  2  0  2  2  2  0  2  0  2  0  0  0  0  2  0  2  2  2  0  2  2  0  2  2  0  2  0  2  2  2  0  0  0  0  0  0  2  2  0  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  2  0  2  2  0  0  0  0  0  0  2  2  0  0  2  0  2  0  2  2  2  2  0  2  2  2  0  0  2  0  2  0  2  0  2  0  0  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  0  0  0  0  2  0  2  2  0  0  2  2  2  0  0  0  2  2  0  2  2  2  0  0  2  0  2  0
 0  0  0  0  0  2  0  0  0  2  0  2  0  0  2  0  0  2  2  2  2  2  2  0  0  0  2  0  0  2  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  0  2  0  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  2  2  2  0  0  2  2  0  2  0  0  0  0  0  2  2  0  0  2  0  2
 0  0  0  0  0  0  0  2  0  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0  0  2  0  2  0  2  2  0  0  0  0  2  0  2
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  0  2  2  2  0  2  0  0  0  0  0  2  0  0  0  2  2  0  2  2  2  2  2  0  2  0  2  2  0  0  0  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+26x^42+12x^43+65x^44+120x^45+96x^46+180x^47+117x^48+476x^49+145x^50+748x^51+173x^52+748x^53+135x^54+476x^55+88x^56+180x^57+76x^58+120x^59+43x^60+12x^61+22x^62+17x^64+9x^66+7x^68+3x^70+1x^80

The gray image is a code over GF(2) with n=208, k=12 and d=84.
This code was found by Heurico 1.16 in 1.08 seconds.