The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+344x^55+1040x^56+2050x^57+2989x^58+3496x^59+4468x^60+4402x^61+4332x^62+3758x^63+2680x^64+1522x^65+871x^66+428x^67+190x^68+102x^69+62x^70+22x^71+5x^72+4x^73+2x^74

The gray image is a code over GF(2) with n=488, k=15 and d=220.
This code was found by Heurico 1.16 in 9.19 seconds.