The generator matrix

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

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+20x^6+18x^7+31x^8+112x^9+665x^10+108x^11+30x^12+16x^13+18x^14+2x^15+2x^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 0.016 seconds.