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

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+160x^56+20x^57+144x^59+145x^60+184x^61+144x^63+127x^64+20x^65+70x^68+8x^72+1x^108

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 0.251 seconds.