The generator matrix

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

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+109x^56+116x^57+186x^58+112x^59+140x^60+72x^61+110x^62+48x^63+41x^64+4x^65+12x^66+32x^67+20x^68+8x^70+9x^72+2x^74+2x^78

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 0.124 seconds.