The generator matrix

 1  0  0  0  1  1  1  1  2  1 X+2  1  2  1  2  1  1 X+2  X  1  1  2  1  0  1  X X+2 X+2  1  1  1  2  X  2  1  1  2  1  1  1  1  2  1  2  1  1  X X+2  1  0  1  1  1  1  1  1  1  1  X  1  2  1
 0  1  0  0  0  2  1  3  1 X+2  0 X+3  1 X+3  1  X  2  X  1  2 X+1  X X+1  1  X  1  0  X X+1  X  3  1  1  2  3  3  1 X+2  3 X+2  0  1 X+2  1  X X+3  1  2  2  1  1  0 X+1  1  2 X+2  3 X+3  1  1  2  X
 0  0  1  0  0  3  1  2  3  1  1  0  X X+1 X+1  X  X  1  2  1  1  0  X  2 X+1  1  1  0 X+2 X+3 X+1  0  1  1  1  3 X+3 X+3  2 X+3  X  3  2 X+3  X X+1  X  1  0  1 X+3  X X+2 X+2  2 X+2 X+3  1  3  0  1  X
 0  0  0  1  1  1  2  3  3  X X+1  2 X+3  1  X X+1  2  3  3  X X+1  1 X+2  2 X+3  X  2  1  1 X+2 X+2 X+3  1  1  2 X+3  1 X+3 X+1  0  2 X+2 X+3 X+2 X+2  1 X+1 X+3 X+1  1 X+3  X X+1  X X+3  3  0 X+3  0  X X+2  3
 0  0  0  0  X  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  2  X  X X+2 X+2  X X+2  X X+2 X+2 X+2 X+2 X+2 X+2  X  2  X X+2  0  X X+2 X+2 X+2  2 X+2  2 X+2  X  2  2  X  0  X X+2  2 X+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+203x^54+416x^55+743x^56+858x^57+1230x^58+1282x^59+1414x^60+1244x^61+1588x^62+1472x^63+1507x^64+1236x^65+1095x^66+718x^67+561x^68+328x^69+279x^70+92x^71+59x^72+26x^73+19x^74+4x^75+3x^76+4x^77+2x^82

The gray image is a code over GF(2) with n=248, k=14 and d=108.
This code was found by Heurico 1.13 in 4.15 seconds.