The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  1 X+2  0  1  0  1  1  1 X+2  X  X  0 X+2  2  1  X  1  0  0  1  1  1  2  1  2 X+2  1  1  1  0  1  1  X  1  0  X  1  0  0  2  X X+2  1  X  X  2  1  1  1
 0  1  0  0  0  0  0  0  0  2  2  2  2  0  0 X+3  1 X+1  3  1  1  1  1  1  1  1  1  X  X  X X+2 X+3  1  X  1  1  1 X+2  0 X+2 X+2  2  X X+1  1  0  X  1  3  1  X  1  1  1  1  2  1  0 X+3  1  0
 0  0  1  0  0  2  1  3  1  X  0 X+1 X+3  1  1 X+2 X+1  2  1  1  0 X+1 X+2 X+2  1  1 X+2  0 X+2  1  1  1 X+3  X  0 X+1 X+2  0 X+3  3  1  1 X+1 X+1 X+3  1  0  2 X+1  1  0 X+3  2 X+3  0  1 X+2  1 X+3  X  0
 0  0  0  1  0  3  1  2  3  0 X+1  X  3  0 X+3  2  3 X+3  0 X+1  3 X+2  X X+1 X+3  X  X  1  3 X+1  3  3  0  2  1 X+2  0  1 X+1  X X+3 X+1  2  X X+3  X  1  1  0 X+3  1  1  X  X X+1  0  2  2 X+1 X+1  2
 0  0  0  0  1  1  2  3  3 X+1  X  0  3 X+3  X  2  3  1 X+2 X+3  1  0 X+3 X+2  0 X+3  1 X+3  0  1 X+2  X X+2  1  1  1  2  X  3 X+2  2  2 X+1 X+1  1 X+2 X+1  0  1  0  3 X+1  3 X+1  0  2 X+2 X+1 X+3 X+1  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+144x^52+516x^53+886x^54+1330x^55+1515x^56+2052x^57+2365x^58+2928x^59+3098x^60+3222x^61+2964x^62+3004x^63+2456x^64+2192x^65+1429x^66+1090x^67+758x^68+436x^69+176x^70+78x^71+54x^72+44x^73+16x^74+2x^75+6x^76+2x^77+4x^78

The gray image is a code over GF(2) with n=244, k=15 and d=104.
This code was found by Heurico 1.13 in 14.6 seconds.