The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+32x^61+22x^62+5x^64+2x^66+2x^68

The gray image is a code over GF(2) with n=488, k=6 and d=244.
This code was found by Heurico 1.16 in 0.141 seconds.