The generator matrix

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

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+150x^54+116x^55+489x^56+300x^57+716x^58+440x^59+814x^60+736x^61+922x^62+564x^63+860x^64+524x^65+576x^66+272x^67+300x^68+104x^69+142x^70+16x^71+79x^72+44x^74+14x^76+10x^78+3x^80

The gray image is a code over GF(2) with n=248, k=13 and d=108.
This code was found by Heurico 1.16 in 4.17 seconds.