The generator matrix
1 0 0 1 1 1 2 2 3X+2 1
0 1 0 1 X 3X+3 0 1 3X+2 0
0 0 1 1 1 0 1 1 1 0
0 0 0 X 2X 3X 3X+2 2X+2 X+2 2X
generates a code of length 10 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+92x^6+402x^7+2171x^8+6616x^9+14173x^10+6684x^11+2146x^12+376x^13+102x^14+2x^15+2x^16+1x^18
The gray image is a code over GF(2) with n=80, k=15 and d=24.
This code was found by Heurico 1.16 in 0.718 seconds.