The generator matrix

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

generates a code of length 5 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+59x^4+136x^5+58x^6+2x^8

The gray image is a code over GF(2) with n=40, k=8 and d=16.
This code was found by Heurico 1.16 in 6.87e-008 seconds.