The generator matrix

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

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+32x^45+135x^46+236x^47+290x^48+388x^49+389x^50+398x^51+487x^52+382x^53+348x^54+366x^55+245x^56+182x^57+101x^58+28x^59+22x^60+18x^61+17x^62+10x^63+10x^64+6x^65+2x^67+1x^68+2x^70

The gray image is a code over GF(2) with n=208, k=12 and d=90.
This code was found by Heurico 1.16 in 0.675 seconds.