The generator matrix

 1  0  1  1  1  0  X  X
 0  1  1  0 X+1  1  0  0
 0  0  X X+2  0 X+2  X  0
 0  0  0  2  0  0  0  2
 0  0  0  0  2  0  0  2
 0  0  0  0  0  2  0  2
 0  0  0  0  0  0  2  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+100x^4+32x^5+672x^6+480x^7+1526x^8+480x^9+672x^10+32x^11+100x^12+1x^16

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 0.00941 seconds.