The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+98x^7+641x^8+1538x^9+3652x^10+1530x^11+622x^12+94x^13+12x^14+4x^15

The gray image is a code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.047 seconds.