The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X  X  1  1  X  2  1  1  2  1  0  1  2  1  1  1 X+2  0  2  1  1  1  1  X  2  1  1  2  0  1  0  1  1 X+2 X+2  0  1  2  X  X  1  2  2  2  0  0  0  1
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1  1  1  X  1  1 X+2  1  0  0 X+3  1  2  1  X  X  1 X+3 X+1  1  1  1  0 X+3  3  2  1  1 X+3 X+2  1  X  X  1 X+3 X+3  1  1  X  0  0  0  1  2  1  1  2  1  1  1  0
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  1  0  X X+1  1  2  X  0  1  1 X+1  1  X  1 X+1  X  1  1  0 X+1 X+3 X+2 X+1  2 X+3 X+3 X+2  3  0 X+2  3  2  1 X+3  2  1  X  3  1  1 X+1  1  1 X+2  0  3  1  1  2  2  0  0
 0  0  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  2  0  2  2  2  0  2  2  2  2  2  0  2  0  2  0  0  0  0  0  2  0  2  2  2  0  2  2  0  2  2  0  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  2  0  2  0  2  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  2  2  0  2  0  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  0  2  2  2  0  2  0  2  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  2  0  0  2  2  0  0  2  2  0  0  0  0  2  2  0  2  2  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  2  2  2  0  2  2  0  2  2  0  2  0  0  0  0  2  2  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  0
 0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  0  0  2  2  0  2  0  0  0  2  0  2  2  2  0  0  0  2  2  0  0  0  2  2  2  0  2  0  2  2  0  2  2  2  0  2  0  2  0  2  2  0  0  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+20x^52+118x^53+222x^54+426x^55+606x^56+816x^57+1054x^58+1230x^59+1435x^60+1514x^61+1553x^62+1564x^63+1458x^64+1240x^65+1069x^66+748x^67+500x^68+362x^69+172x^70+106x^71+60x^72+40x^73+20x^74+22x^75+11x^76+6x^77+5x^78+3x^80+1x^82+2x^84

The gray image is a code over GF(2) with n=248, k=14 and d=104.
This code was found by Heurico 1.16 in 11.6 seconds.