The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^2+52x^4+116x^6+512x^7+662x^8+512x^9+116x^10+52x^12+12x^14+1x^16

The gray image is a code over GF(2) with n=32, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00208 seconds.