The generator matrix

 1  0  0  1  1  1 X+2  1  1  X  1  2  1  2  1  2  X  1 X+2  1  1  1  0  X  1  1  2 X+2  1  1 X+2  1  X  1  1  2  1  1  1  1  X  1  1  2  1  0  X  1  0  1  1  1  0  1  1  X X+2  X X+2  1  1  1
 0  1  0  0  1 X+3  1 X+2 X+3  1  3  1  X  X  2  1  1  X  1  1  1  3  2  1 X+1  0  1  2 X+1 X+1  2  X  1 X+2  2  1 X+3  0  0  X  1  2  X  2 X+1  1  1 X+1  1 X+2  3  3  1  1 X+2  1  1  1  0  3  1  2
 0  0  1  1 X+1  0 X+3  1 X+3 X+2  X  3  X  1  0  2  3 X+1 X+1 X+2  1 X+3  1  2  X  3  X  1  1  2  1  3  1 X+2 X+2  0 X+2 X+1  1 X+1  X  3  X  1  X X+3  3 X+3  1  2  0  1  2 X+2 X+2  3  0 X+2  1  1 X+3 X+2
 0  0  0  X  X X+2  0 X+2 X+2  0 X+2  2  2  0 X+2 X+2  X  0 X+2  2  0  0  X X+2 X+2  0  2  0 X+2  2 X+2  2  0  2 X+2 X+2  2 X+2 X+2  X  X  0 X+2  X  0 X+2  X X+2 X+2 X+2  2  X  X X+2 X+2 X+2 X+2  0  X  0  0  X
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  0  0  2  0  2  2  2  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  0  0  2  0  2  0  2  2  2  0  2  2  0  2  2  0  2  2
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  0  0  2  2  0  2  2  0  2  2  2  2  0  2  2  2  0  2  0  0  0  0  2  0  0  0  0  2  0  2  0  2  0  2  2  2
 0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  0  0  2  2  0  2  0  0  0  0  2  2  0  2  0  2  0  0  2  0  0  0  2  0  2  0  0  2  0  0  2  0  2  2  2  0  2  2  0  2  2  2  2  0  0  2

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+60x^53+208x^54+474x^55+625x^56+860x^57+1020x^58+1158x^59+1430x^60+1612x^61+1679x^62+1550x^63+1427x^64+1146x^65+1046x^66+788x^67+488x^68+382x^69+168x^70+102x^71+57x^72+34x^73+38x^74+22x^75+2x^76+2x^77+1x^78+2x^79+2x^80

The gray image is a code over GF(2) with n=248, k=14 and d=106.
This code was found by Heurico 1.16 in 12.1 seconds.