The generator matrix

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

generates a code of length 6 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+28x^2+16x^3+71x^4+240x^5+312x^6+240x^7+71x^8+16x^9+28x^10+1x^12

The gray image is a code over GF(2) with n=24, k=10 and d=4.
This code was found by Heurico 1.16 in 0.000506 seconds.