The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+82x^45+298x^46+490x^47+611x^48+706x^49+750x^50+856x^51+913x^52+794x^53+681x^54+586x^55+510x^56+398x^57+192x^58+124x^59+97x^60+44x^61+31x^62+8x^63+12x^64+8x^65

The gray image is a code over GF(2) with n=208, k=13 and d=90.
This code was found by Heurico 1.16 in 2.72 seconds.