The generator matrix

 1  1  1  1  X  0  X  X  X  X
 0  X 2X+2 X+2 X+2  X 3X X+2  0  0
 0  0 2X  0  0  0 2X 2X  0  0
 0  0  0 2X  0  0 2X 2X 2X  0
 0  0  0  0 2X  0  0 2X 2X  0
 0  0  0  0  0 2X 2X  0 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+25x^6+48x^7+128x^8+592x^9+463x^10+592x^11+124x^12+48x^13+23x^14+3x^16+1x^18

The gray image is a code over GF(2) with n=80, k=11 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.