The generator matrix

 1  0  0  1  1  1  1 3X  1  1
 0  1  0  1 X+2 X+3 2X+2  1 X+2  0
 0  0  1  1 X+1  X  X  1  0  0
 0  0  0 2X+2  0 2X  2  2 2X 2X

generates a code of length 10 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+73x^6+154x^7+1067x^8+3424x^9+6914x^10+3444x^11+1106x^12+144x^13+53x^14+2x^15+2x^16

The gray image is a code over GF(2) with n=80, k=14 and d=24.
This code was found by Heurico 1.16 in 0.172 seconds.