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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  2  X  X  X  X  X  X  X  X  X  X  X  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  2  0  2  2  2  2  0  0  2  0  2  0  2  0  0  0  0  0  2  2  2  2  0  0
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  2  2  2  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  0  2  2  0  0  2  2  0  0  2  0  2  0  0  0  2  2  0  2  2  0  0  0
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  2  0  2  2  0  2  0  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+10x^56+30x^57+10x^58+64x^59+12x^60+94x^61+12x^62+9x^64+2x^65+10x^66+2x^85

The gray image is a code over GF(2) with n=240, k=8 and d=112.
This code was found by Heurico 1.16 in 0.0901 seconds.