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

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+90x^52+90x^53+181x^54+220x^55+260x^56+442x^57+380x^58+616x^59+701x^60+702x^61+912x^62+710x^63+688x^64+622x^65+396x^66+406x^67+216x^68+136x^69+145x^70+86x^71+74x^72+48x^73+21x^74+10x^75+17x^76+8x^77+10x^78+1x^80+2x^82+1x^90

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 5.42 seconds.