The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+275x^56+710x^58+868x^60+712x^62+670x^64+390x^66+276x^68+132x^70+46x^72+8x^74+7x^76+1x^84

The gray image is a code over GF(2) with n=248, k=12 and d=112.
This code was found by Heurico 1.16 in 0.778 seconds.