The generator matrix

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

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+106x^56+330x^57+376x^58+470x^59+369x^60+438x^61+357x^62+306x^63+279x^64+260x^65+226x^66+178x^67+127x^68+126x^69+52x^70+54x^71+20x^72+14x^73+2x^74+2x^76+3x^78

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 0.642 seconds.