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

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

Homogenous weight enumerator: w(x)=1x^0+135x^56+456x^60+256x^62+87x^64+88x^68+1x^120

The gray image is a code over GF(2) with n=244, k=10 and d=112.
This code was found by Heurico 1.16 in 9.95 seconds.