The generator matrix

 1  0  1  1  1  2  X  1  1  1 X+2  1  1  1  2  1  1  2  1  1 X+2  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  0 X+2  1 X+2  0  1  2  0  1  1  2
 0  1  1 X+2 X+3  1  1 X+1  X  3  1  X  X X+1  1  2 X+1  1  0  1  1  0  1  1  0 X+2  2  X X+1  3 X+3  1  0 X+2  0 X+2 X+1  3 X+3  1  0  2 X+2  2 X+2  0 X+2  X  2  X  1  2  1  1 X+2  2  1 X+2  2  X
 0  0  X  0 X+2  X  X  2  X  2  0 X+2  0  2 X+2  X  X  0  0 X+2  0 X+2  2 X+2  0  2  X X+2  0  2  X  X  0  2  X X+2  2  0  X  X  X  2  0 X+2  X  2  0  X X+2  2  0  0  2  2  X  X  0 X+2  2  0
 0  0  0  2  0  2  2  2  0  2  0  0  2  0  0  2  2  2  0  2  2  2  0  0  2  0  0  2  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  2  2  0  2  0  2  2  0  2  0  0  0  0  0  0  2
 0  0  0  0  2  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  0  2  0  0  2  2  2  0  2  0  0  0  0  2  2  2  2  0  0  0  0  2  0  2  2  2  2  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+281x^56+64x^58+376x^60+64x^62+200x^64+28x^68+4x^72+4x^76+1x^80+1x^88

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 5.35 seconds.