The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 1 1 X 1 1 X X 1 X 2 0 X 1 X 1 2 0 X X 1 2 X 2 0 X 2 X 2 X X 2 0
0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 2 0 2 0 2 2 0 2 2 0 2 0 2 0 0 2 2 2 2 0 0 2 2 2 0 2 0 0 2 2 2 0 0 0 0 2 2 2
generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 59.
Homogenous weight enumerator: w(x)=1x^0+8x^59+5x^60+2x^62
The gray image is a code over GF(2) with n=224, k=4 and d=118.
This code was found by Heurico 1.16 in 0.063 seconds.