The generator matrix

 1  0  0  1  1  1 X^3+X^2 X^3+X^2 X^2+X  1
 0  1  0  1  X X^2+X+1  0  1 X^2+X  0
 0  0  1  1  1  0  1  1  1  0
 0  0  0  X X^3 X^3+X X^2+X X^2 X^2+X X^3

generates a code of length 10 over Z2[X]/(X^4) 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 linear code over GF(2) with n=80, k=15 and d=24.
This code was found by Heurico 1.16 in 0.656 seconds.