The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+83x^4+128x^5+422x^6+896x^7+1031x^8+896x^9+436x^10+128x^11+69x^12+6x^14

The gray image is a code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00929 seconds.