The generator matrix

 1  0  0  1  1  1  X  1
 0  1  0  1 X+2 X+3  1  0
 0  0  1  1 X+3 X+2  1  0
 0  0  0  2  0  0  2  0
 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+55x^4+160x^5+598x^6+352x^7+1759x^8+352x^9+612x^10+160x^11+41x^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 0.00756 seconds.