The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+20x^6+36x^7+25x^8+24x^9+12x^10+4x^11+6x^12

The gray image is a code over GF(2) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in 0.000229 seconds.