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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+49x^52+160x^53+147x^54+154x^55+298x^56+420x^57+554x^58+550x^59+590x^60+762x^61+856x^62+840x^63+672x^64+530x^65+472x^66+326x^67+207x^68+198x^69+115x^70+100x^71+84x^72+34x^73+30x^74+12x^75+17x^76+8x^77+2x^78+2x^79+1x^80+1x^92

The gray image is a code over GF(2) with n=248, k=13 and d=104.
This code was found by Heurico 1.16 in 5.13 seconds.