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.