The generator matrix

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

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+50x^53+104x^54+198x^55+245x^56+384x^57+594x^58+636x^59+769x^60+816x^61+779x^62+750x^63+758x^64+616x^65+477x^66+416x^67+221x^68+170x^69+64x^70+42x^71+41x^72+8x^73+22x^74+4x^75+9x^76+4x^77+5x^78+2x^79+3x^80+3x^82+1x^84

The gray image is a code over GF(2) with n=248, k=13 and d=106.
This code was found by Heurico 1.16 in 4.22 seconds.