The generator matrix

 1  0  0  1  1  1 X+2  X
 0  1  0  0  1 X+3  1  2
 0  0  1  1  1  0  1  0
 0  0  0  X  0 X+2 X+2  X
 0  0  0  0  2  0  0  2
 0  0  0  0  0  2  0  2
 0  0  0  0  0  0  2  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+220x^4+256x^5+2688x^6+1792x^7+6470x^8+1792x^9+2688x^10+256x^11+220x^12+1x^16

The gray image is a code over GF(2) with n=32, k=14 and d=8.
This code was found by Heurico 1.16 in 3.29 seconds.