The generator matrix

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

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+18x^3+71x^4+202x^5+726x^6+1828x^7+2495x^8+1828x^9+740x^10+202x^11+57x^12+18x^13+6x^14

The gray image is a code over GF(2) with n=32, k=13 and d=6.
This code was found by Heurico 1.16 in 0.0374 seconds.