The generator matrix

 1  0  0  0  1  1  1  1
 0  1  0  0  X  1  X  2
 0  0  1  0 X+1  1  1 X+1
 0  0  0  1  1 X+2  0  X
 0  0  0  0  2  0  2  2
 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 4.

Homogenous weight enumerator: w(x)=1x^0+147x^4+384x^5+1830x^6+3200x^7+5255x^8+3200x^9+1844x^10+384x^11+133x^12+6x^14

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 0.145 seconds.