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  0  1  1  1  1  1  1  1  X  1  1  1  1  2  1  X  1  1  1  1  0  1  1  2  0  1  X  1  1  1  1  1  1
 0  X  0  0  0  2  0  2  0  X  X  X X+2 X+2  X  X  2  2 X+2  2 X+2  X X+2  0  0  X  0 X+2  2  X  2 X+2  2  X  2  X  0  0  X  2  X  0  X  0  2  0  0  X  X  X X+2  X  2  X  2  0  X  2  0  2  0  2
 0  0  X  0  0  2  X  X  X X+2  X  2 X+2  X  2  2 X+2  X  0  X  0  0  X  0 X+2  2  0 X+2  0  0  2 X+2  X  X  0 X+2  X  X X+2 X+2 X+2  0  2  2 X+2  0  2  0  X  X  X  2  X  X  0  X  X  2  0  0  2  X
 0  0  0  X  0  X  X X+2  2  0  0 X+2  X  X  X  2  X  0  2 X+2  X  2  2  X  2  X  2 X+2  X X+2  0  X  0  0 X+2  X X+2  X  2 X+2 X+2  X X+2 X+2 X+2  0  2  X  X  2  2 X+2  2  2  X  2  X  2  0  0  0  2
 0  0  0  0  X  X  2  X X+2  X  0 X+2  X  0  2  X X+2  X  X  2  0  2  0  X  0 X+2  X  0  2  X  2 X+2  0 X+2  0 X+2  0  2  X X+2  0  2  2  X X+2  2  X  X X+2 X+2  2  X  X  0 X+2  0  X  X X+2 X+2  X  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+264x^56+12x^57+164x^59+300x^60+312x^61+392x^63+223x^64+124x^65+20x^67+156x^68+72x^72+7x^76+1x^108

The gray image is a code over GF(2) with n=248, k=11 and d=112.
This code was found by Heurico 1.16 in 40 seconds.