The generator matrix

 1  0  1  1  1  2  1  1  X  1  1 X+2  X  1  1  0  1  1 X+2  1  1  1  1  2  X X+2  X  X  X  2  2  2  X  2  X  2  0 X+2  2 X+2  0  2  X  1  1  1  1  1  1  2  1  1  0  1  X X+2  1  0  1  1
 0  1  1  0 X+1  1 X+3  0  1  2  1  1  1  X  3  1  X X+1  1 X+2 X+1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2 X+3  1  0  X  1  1  3  1  1  1  1 X+3  1  X  2
 0  0  X  0  0  0  0  X X+2  X  X  X X+2 X+2  2  2  2 X+2 X+2 X+2 X+2  2  2  2 X+2  0  2  0  0  X X+2 X+2  2  X  2 X+2  X X+2  2  2  X X+2  0  0 X+2  2  X  X  0  0 X+2  2  0  0 X+2  X  0  2  X  X
 0  0  0  X  2 X+2 X+2  X  2  2 X+2  X  0  0  0  2  2  2  X X+2  X X+2  X X+2 X+2  0  0  X X+2  0  2  X  2 X+2 X+2 X+2  2  2  2  X  X  0  2  2 X+2  X  2  0  X  X  X  2  X  0  X  2  X  0 X+2  0

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+210x^56+56x^57+108x^58+72x^59+172x^60+72x^61+72x^62+56x^63+177x^64+12x^66+10x^68+4x^72+2x^92

The gray image is a code over GF(2) with n=240, k=10 and d=112.
This code was found by Heurico 1.16 in 0.146 seconds.