The generator matrix
1 0 1 1 1
0 1 X+1 3X+2 2
generates a code of length 5 over Z4[X]/(X^2+2X+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 1.05e-007 seconds.