The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+210x^54+360x^55+819x^56+780x^57+1407x^58+1084x^59+1426x^60+1360x^61+1576x^62+1420x^63+1551x^64+1108x^65+1196x^66+680x^67+666x^68+264x^69+253x^70+100x^71+73x^72+8x^73+29x^74+4x^75+4x^76+4x^80+1x^86

The gray image is a code over GF(2) with n=248, k=14 and d=108.
This code was found by Heurico 1.16 in 10.3 seconds.