The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^2+160x^3+598x^4+160x^5+52x^6+1x^8

The gray image is a code over GF(2) with n=32, k=10 and d=8.
This code was found by Heurico 1.16 in 3.62e-008 seconds.