The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X  X  1  1  2  1  1  X  X  0  1  2  1  1  0  1  1  1  2  X  1  1  1  X  1  X  1  1  2  1  1  1  0  2  0  0  1  0  1  0  1  1  X  0  1  2  1
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1  1  1  X  1  1 X+2  1  0  3  1  1  X X+1  1  2  0  1  X  X  3  1  X X+1  0 X+1 X+2  2  1 X+1  X X+2 X+2 X+3  3  1  1  2 X+2  X  1 X+2  1 X+1  1  1  1 X+1  X X+3
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  1  0  X X+1  1  2  X  0 X+3 X+3 X+1  2  3  1 X+3  1  1  3  1  X X+2  0  0  1  2 X+2  1  1 X+1 X+2 X+1  3  1  X  0  X  3 X+2  1  1 X+3  0 X+2 X+3 X+3  X X+3 X+2  2  1  2
 0  0  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  2  0  0  0  2  2  0  0  2  0  0  0  2  0  0  0  0  0  2  2  0  2  0  0  0  2  0  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  2  2  0  2  0  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  2  0  0  2  0  0  2  0  0  2  0  2  0  0  2  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  0  2  2  2  2  2  2  2  0  0  2  2  0  0  0  2  0  0  2  0  2  0  2  0  2  2  2  2  2  2  2  0  2  2  0  2  2  2  2  2  2  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  2  0  0  2  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  2  2  2  2  0  0  2  0  2  2  2  0  0  2  2  2  2  0  0
 0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  2  2  0  0  2  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  2  0  0  0  2  0  2  2  0  2  2  2  2  0  0  0  0  0  0  0  2  0  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+77x^52+230x^53+353x^54+696x^55+751x^56+1218x^57+1087x^58+1534x^59+1312x^60+1814x^61+1375x^62+1704x^63+1147x^64+1158x^65+641x^66+610x^67+259x^68+172x^69+101x^70+54x^71+29x^72+16x^73+23x^74+8x^75+8x^76+3x^78+2x^79+1x^82

The gray image is a code over GF(2) with n=244, k=14 and d=104.
This code was found by Heurico 1.16 in 11.9 seconds.