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

generates a code of length 61 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+230x^52+428x^54+56x^55+648x^56+244x^57+788x^58+416x^59+1011x^60+612x^61+1028x^62+440x^63+823x^64+220x^65+550x^66+48x^67+322x^68+12x^69+178x^70+96x^72+30x^74+4x^76+6x^78+1x^92

The gray image is a code over GF(2) with n=244, k=13 and d=104.
This code was found by Heurico 1.16 in 7.93 seconds.