The generator matrix

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

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+20x^7+162x^8+480x^9+704x^10+520x^11+152x^12+4x^15+5x^16

The gray image is a code over GF(2) with n=80, k=11 and d=28.
This code was found by Heurico 1.16 in 0.141 seconds.