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  X  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  2  X  1  2  1
 0 2X+2  0  0  0  2 2X+2  2  0 2X 2X  0  2  2 2X+2 2X+2  0 2X  0  2 2X 2X+2 2X+2  2  0  2 2X+2 2X 2X  2 2X  2  2  2  0  0 2X+2 2X  2 2X 2X+2  0  0 2X+2 2X+2  0 2X+2 2X+2 2X  0  0  0 2X  2  2 2X  2  0 2X+2 2X  2
 0  0 2X+2  0  2  2  2 2X 2X+2 2X  0  2  2  2  0  0  0 2X 2X+2 2X+2  2  2  0 2X  2  0 2X+2  0 2X+2 2X 2X 2X+2  0  2 2X 2X+2  2 2X  0 2X+2 2X 2X  0  2 2X 2X+2 2X+2 2X+2  0  2 2X+2 2X+2  2  0  0 2X+2  2  2 2X 2X+2  0
 0  0  0 2X+2  2 2X 2X+2 2X+2  0  0  2  2  0 2X+2  2 2X  0 2X+2  2  2 2X  0 2X+2 2X 2X+2 2X+2  0 2X  0 2X  2  2 2X  2  2 2X+2 2X 2X 2X+2 2X 2X  2 2X 2X 2X+2 2X+2  2 2X+2  2 2X  0 2X 2X  0 2X 2X+2 2X  2  2  2 2X
 0  0  0  0 2X 2X 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X  0  0 2X  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  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+160x^56+64x^58+96x^59+596x^60+320x^61+448x^62+96x^63+188x^64+68x^68+10x^72+1x^112

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 0.469 seconds.