The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+14x^34+1x^36

The gray image is a code over GF(2) with n=128, k=4 and d=68.
This code was found by Heurico 1.16 in 0.00778 seconds.