The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+22x^59+2x^60+4x^62+2x^63+1x^64

The gray image is a code over GF(2) with n=232, k=5 and d=118.
This code was found by Heurico 1.16 in 0.0726 seconds.