The generator matrix

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

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+126x^56+308x^57+396x^58+376x^59+472x^60+382x^61+406x^62+300x^63+304x^64+216x^65+214x^66+198x^67+126x^68+90x^69+106x^70+36x^71+15x^72+12x^73+6x^74+2x^75+4x^76

The gray image is a code over GF(2) with n=248, k=12 and d=112.
This code was found by Heurico 1.11 in 0.334 seconds.