The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+94x^52+356x^54+32x^55+501x^56+156x^57+722x^58+264x^59+985x^60+596x^61+1022x^62+464x^63+885x^64+388x^65+688x^66+136x^67+372x^68+12x^69+272x^70+139x^72+70x^74+28x^76+6x^78+2x^80+1x^92

The gray image is a code over GF(2) with n=248, k=13 and d=104.
This code was found by Heurico 1.16 in 5.33 seconds.