The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  1 X+2  1  X  1  1  X  X  1  1  1  1  2  2  1  1  X  2  1  1  2  1  1 X+2  1  1  1  1  1  X  1  1  1  1  1  1  X  2  1  1  1  X  1  2  1  X  1  2  1
 0  1  1  0  1  1  2 X+1  1  0  1  3 X+3  0  1  1  1  2  2  1  1 X+1  2  3  3  1  1  0 X+2  1  1 X+1  0  1 X+1  2  1 X+1  2  0  X  X  1  1  X  3  3  1 X+3  1  X  3  0 X+1  1 X+1  X  3  1  X  1  0
 0  0  X  0  0  0  0  0  0  0  0  0  2  X X+2 X+2 X+2 X+2 X+2  X  X X+2  X  X  2  2  2  X  0  2 X+2  X  0  X  2 X+2  2  X  0  2  X  2 X+2  0 X+2  0  0  2  2  0  2  2  2 X+2  X  0 X+2  2 X+2  0 X+2  0
 0  0  0  X  0  0  0  0  X X+2 X+2  X X+2 X+2 X+2 X+2  0 X+2  2 X+2  2 X+2  0  0  2  X  0  0  2  2  X  0 X+2  2 X+2  X X+2  X X+2  2  0  X  X  X X+2  X X+2  0  2 X+2  X  X  2  2 X+2  2  0  0  2  2  2  2
 0  0  0  0  X  0  2 X+2  0  2  0 X+2  X  X  X  2  X X+2  X  X  X  0 X+2  2  0 X+2  X  2  X X+2  2  X  X  X  X  0  X  X X+2 X+2 X+2  2  2  2  X  X  X  2 X+2  0  2  X  0  0 X+2  0  X  0  X  0  X  0
 0  0  0  0  0  X X+2 X+2 X+2 X+2  2  2  X X+2 X+2  2  2  0 X+2  0  X X+2  0 X+2  2  X  X  X X+2  0  2  X X+2  X  2 X+2  0  X  X  0  0 X+2 X+2  2  0 X+2  0 X+2  2  0  X X+2  0  X  0  2  2  X  0  X X+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+59x^52+136x^53+246x^54+350x^55+585x^56+722x^57+972x^58+1266x^59+1518x^60+1618x^61+1583x^62+1674x^63+1364x^64+1284x^65+1021x^66+686x^67+501x^68+280x^69+197x^70+104x^71+83x^72+50x^73+37x^74+16x^75+14x^76+6x^77+6x^78+3x^80+2x^82

The gray image is a code over GF(2) with n=248, k=14 and d=104.
This code was found by Heurico 1.16 in 13.5 seconds.