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  X  1  1  1  X  1  0  1  2  1  X  2  X  2  X  X  X  X
 0  X  0  0  0  X X+2  X  2  0  X X+2  0  2  X X+2  X  0  2 X+2  2  X  X  0  2 X+2  0  X  2 X+2  X  2  0  0  2 X+2  0  X X+2  X  X X+2 X+2  2 X+2  0 X+2  X  X  2  X  0  X  X X+2  X  2  0  0  2
 0  0  X  0  X  X  X  0  X X+2  X X+2  0  2  0  2 X+2  0  X  X X+2  0  2  0  0  2  2  2  X X+2 X+2  X X+2  X X+2  X  X X+2  0  2  0  2  0  0  X  2  2 X+2  2  0  0  2  0  2  2  0  X X+2 X+2 X+2
 0  0  0  X  X  2 X+2  X  0 X+2  0 X+2  0 X+2 X+2  2  X  2 X+2  0  0  X  2  X X+2  0  2 X+2  X  2  X  2  0  X  X X+2  2 X+2  0  0 X+2 X+2  2  0  2  0  2  2  0  X  0  X X+2 X+2 X+2  X  0  0  2  2
 0  0  0  0  2  2  2  0  2  0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  0  0  0  2  0  0  2  2  0  0  2  0  0  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+334x^56+128x^58+128x^60+128x^62+286x^64+18x^72+1x^96

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 77.6 seconds.