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

generates a code of length 62 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+57x^56+114x^58+32x^59+210x^60+352x^61+562x^62+352x^63+197x^64+32x^65+60x^66+37x^68+26x^70+8x^72+6x^74+1x^76+1x^112

The gray image is a code over GF(2) with n=496, k=11 and d=224.
This code was found by Heurico 1.16 in 0.313 seconds.