The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+486x^56+1028x^57+1680x^58+2030x^59+2136x^60+2188x^61+2301x^62+1624x^63+1163x^64+816x^65+500x^66+200x^67+144x^68+28x^69+26x^70+16x^71+6x^72+4x^73+4x^74+2x^75+1x^78

The gray image is a code over GF(2) with n=488, k=14 and d=224.
This code was found by Heurico 1.16 in 2.63 seconds.