The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+62x^53+196x^54+458x^55+598x^56+854x^57+1089x^58+1316x^59+1428x^60+1480x^61+1641x^62+1456x^63+1409x^64+1206x^65+1059x^66+830x^67+523x^68+352x^69+161x^70+116x^71+63x^72+44x^73+12x^74+14x^75+9x^76+2x^77+2x^78+2x^79+1x^80

The gray image is a code over GF(2) with n=248, k=14 and d=106.
This code was found by Heurico 1.16 in 11.5 seconds.