The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  1  X  X  X  1  1  1  1  X  2  2  2  0  0  0  X  X  X  X  1  1  1  1  X  2  2  X  X  2  0  0
 0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  0  0  2  2  0  0  0  2  0  2  2  0
 0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  0  0  2  2  2  2  2  2

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+24x^58+4x^60+3x^64

The gray image is a code over GF(2) with n=228, k=5 and d=116.
This code was found by Heurico 1.16 in 0.0679 seconds.