The generator matrix

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

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+48x^56+282x^57+38x^58+16x^59+40x^60+1102x^61+40x^62+208x^63+39x^64+182x^65+49x^66+2x^69+1x^114

The gray image is a code over GF(2) with n=488, k=11 and d=224.
This code was found by Heurico 1.16 in 0.266 seconds.