The generator matrix

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

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+206x^56+184x^57+452x^58+324x^59+504x^60+340x^61+478x^62+244x^63+336x^64+224x^65+248x^66+132x^67+193x^68+76x^69+94x^70+4x^71+31x^72+8x^73+8x^74+7x^76+2x^80

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 0.799 seconds.