The generator matrix

 1  0  0  0  1  1  1  X  1  1
 0  1  0  0  2  3  1  1 3X  0
 0  0  1  0  3  1  X X+1  3 X+3
 0  0  0  1  1  X X+1  1  3  2
 0  0  0  0 2X  0 2X  0  0 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+197x^6+1756x^7+8240x^8+29952x^9+50711x^10+30072x^11+8236x^12+1696x^13+195x^14+12x^15+3x^16+1x^18

The gray image is a code over GF(2) with n=80, k=17 and d=24.
This code was found by Heurico 1.16 in 16.9 seconds.