The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+33x^6+64x^7+61x^8+64x^9+30x^10+2x^12+1x^14

The gray image is a code over GF(2) with n=32, k=8 and d=12.
This code was found by Heurico 1.16 in 0.000392 seconds.