The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1  X  X X+1  0
 0  0  1  1  1 X+1  0  0
 0  0  0  X  0  X  2  0
 0  0  0  0  2  2  0  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+37x^4+116x^5+370x^6+912x^7+1227x^8+904x^9+380x^10+112x^11+31x^12+4x^13+2x^14

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 0.00872 seconds.