The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+36x^3+186x^4+934x^5+3369x^6+6960x^7+9781x^8+6980x^9+3378x^10+924x^11+176x^12+38x^13+5x^14

The gray image is a code over GF(2) with n=32, k=15 and d=6.
This code was found by Heurico 1.13 in 0.0315 seconds.