The generator matrix

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

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+79x^52+126x^53+268x^54+370x^55+672x^56+562x^57+1296x^58+924x^59+1696x^60+1060x^61+2167x^62+1226x^63+1899x^64+890x^65+1221x^66+518x^67+545x^68+260x^69+256x^70+140x^71+82x^72+44x^73+32x^74+22x^75+16x^76+2x^77+5x^78+2x^80+3x^82

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 13.7 seconds.