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  X  X  0  X  1  1  1  1  0  1  1  1  X  1  1  X  1  1  0  0  1  1  0  X  1  X  1  1  X  0  1  X
 0  X  0  X  0  0  X X+2  0  2 X+2  X  0  X  X  0  2  X X+2  2  0  2  X  2  0  X  2  X X+2  0  2 X+2  X  0  2  0  2  X  0  X X+2 X+2 X+2  0 X+2 X+2  0  0  2  X  X  2  X X+2  X X+2  0 X+2  2  2  X  X
 0  0  X  X  0 X+2  X  0  2  X  0  X  0 X+2  2 X+2  X  X  2  2  2  X  0  2  0 X+2 X+2  0  0 X+2  X  0  2 X+2  X  2 X+2  X  X  2  2  X  2  0  0  0  X  X  X  0  0  0  2  0  0  2  2  2  X  X  X  X
 0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  0  0  2  2  0  0  2  2  0  0  2  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  0  0  2  0  0  0  0  2  2  0  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  2  0  2  2  0  0  2  2  2  0  2  2  0  0  2  0  2  0  0  0  2  0  2  0  2  0  0  0  2  0  2  2  2  0  2  2  2
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  2  2  0  2  0  0  0  0  2  0  2  0  2  2  0  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  0  0  2  2  0  0  0  0  2  2  0  2  0  2  2  0  2
 0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  0  0  2  0  2  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  0  2  2  2  2  2  2  2  0  0  2  2  2  0  2  0  0  0  2  2  0  0  2  2  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  0  0  2  2  2  2  0  0  2  2  0  2  0  2  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  0  0  2  2  2  0  2  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+42x^53+119x^54+94x^55+110x^56+186x^57+321x^58+312x^59+266x^60+408x^61+454x^62+416x^63+303x^64+276x^65+265x^66+164x^67+62x^68+90x^69+83x^70+34x^71+24x^72+18x^73+29x^74+4x^75+4x^77+7x^78+2x^80+1x^82+1x^94

The gray image is a code over GF(2) with n=248, k=12 and d=106.
This code was found by Heurico 1.16 in 1.63 seconds.