The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+414x^53+1476x^54+4154x^55+7527x^56+13962x^57+20490x^58+28132x^59+35728x^60+37766x^61+35947x^62+29266x^63+20838x^64+13630x^65+6884x^66+3500x^67+1400x^68+668x^69+223x^70+80x^71+38x^72+8x^73+4x^74+4x^75+2x^76+2x^80

The gray image is a code over GF(2) with n=488, k=18 and d=212.
This code was found by Heurico 1.16 in 503 seconds.