The generator matrix

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

generates a code of length 10 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+25x^6+32x^7+192x^8+992x^9+1615x^10+992x^11+188x^12+32x^13+23x^14+3x^16+1x^18

The gray image is a code over GF(2) with n=80, k=12 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.