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

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

Homogenous weight enumerator: w(x)=1x^0+52x^58+2x^60+4x^62+3x^64+2x^68

The gray image is a code over GF(2) with n=232, k=6 and d=116.
This code was found by Heurico 1.16 in 7.27 seconds.