The generator matrix

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

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+9x^6+56x^7+13x^8+32x^9+6x^10+8x^11+2x^12+1x^14

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 0.000277 seconds.