The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+32x^5+108x^6+224x^7+301x^8+224x^9+92x^10+32x^11+10x^12

The gray image is a code over GF(2) with n=32, k=10 and d=10.
This code was found by Heurico 1.16 in 0.00276 seconds.