The generator matrix

1 1 1 1
0 1 1 0
0 X+3 X+3 1
0 X+3 X+2 0

generates a code of length 4 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+24x^1+220x^2+936x^3+1734x^4+936x^5+220x^6+24x^7+1x^8

The gray image is a code over GF(2) with n=16, k=12 and d=2.
This code was found by an older version of Heurico in 0 seconds.