The generator matrix

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

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+127x^4+456x^5+1618x^6+3680x^7+4671x^8+3568x^9+1676x^10+480x^11+97x^12+8x^13+2x^14

The gray image is a code over GF(2) with n=32, k=14 and d=8.
This code was found by Heurico 1.13 in 0.0255 seconds.