The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+46x^2+296x^4+946x^6+5614x^8+946x^10+296x^12+46x^14+1x^16

The gray image is a code over GF(2) with n=32, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0272 seconds.