The generator matrix

 1  1  1  1  X  2  X  X  X  X
 0 2X+2  0 2X+2 2X+2  2 2X+2 2X+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+16x^7+64x^8+240x^9+335x^10+240x^11+60x^12+16x^13+23x^14+3x^16+1x^18

The gray image is a code over GF(2) with n=80, k=10 and d=24.
This code was found by Heurico 1.16 in 0.015 seconds.