The generator matrix

 1  0  1  1  1 X+2  1  1  2  X  1  1  1  1 X+2 X+2  1  1  1  2  1  1  1  2  2  1  1  1  X  1  1  1 X+2  1  1  1 X+2  1  0  1 X+2  1  1 X+2  1  1 X+2  0  1  1  1 X+2  1  1  1  X  1  1  1  1  1  2
 0  1  1  0 X+3  1  X X+1  1  1  3 X+2 X+3  0  1  1  X  1 X+1  1  X  1  2  1  1  2  3 X+1  1 X+2  1  X  1  X X+2  1  1  1  1 X+1  1  2  1  1  X X+2  1  1 X+2 X+2  3  1  1  2  3  1  1  1  X  0 X+3  X
 0  0  X  0 X+2  0  0  0  2  2  2  0  0  X X+2  X  X X+2 X+2 X+2  X  2  0 X+2  X X+2  0  2  2  X  2  2  X  0  2  X  0  X X+2  0  X X+2  X X+2  X  X  2  0  0  X X+2  0  0  X  2  0  2 X+2 X+2  X X+2 X+2
 0  0  0  X  0  0  X  2 X+2  X  0  0  X  X  X  0  2 X+2 X+2 X+2  X  X  X  X  2  0  2  2  X  0  X  0  2  0 X+2  2  2  X  X X+2  X X+2  2  0  2  0  0  2  0  X  X  0  2  2  2 X+2  2  0 X+2 X+2  2  X
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  0  0  2  0  0  2  0  2  0  2  2  2  0  0  2  0  0  2
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  2  2  2  2  0  0  2  2  2  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  0  0  0  0  2  0  2  2  2  2  2  2  2  0  2  0  2  0  0  2  0
 0  0  0  0  0  0  2  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  0  2  2  0  2  2  0  0  0  2  2  0  2  0  2  0  0  2  2  2  2  2  0  0  2  0  0  0  2  2  0  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+161x^54+84x^55+437x^56+288x^57+713x^58+516x^59+888x^60+584x^61+912x^62+772x^63+794x^64+464x^65+609x^66+284x^67+366x^68+72x^69+120x^70+8x^71+52x^72+42x^74+13x^76+3x^78+8x^80+1x^84

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 6.05 seconds.