The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+41x^54+202x^55+256x^56+600x^57+407x^58+918x^59+648x^60+942x^61+560x^62+900x^63+476x^64+760x^65+322x^66+468x^67+232x^68+236x^69+69x^70+66x^71+42x^72+16x^73+7x^74+6x^75+8x^76+6x^77+2x^78+1x^80

The gray image is a code over GF(2) with n=248, k=13 and d=108.
This code was found by Heurico 1.16 in 2.86 seconds.