The generator matrix

 1  1  1  1  X  1  1  1  1  1
 0 X^3  0  0 X^3  0 X^3 X^3  0  0
 0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0 X^3 X^3 X^3  0 X^3  0  0

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+5x^8+8x^9+101x^10+8x^11+2x^12+2x^14+1x^18

The gray image is a linear code over GF(2) with n=80, k=7 and d=32.
This code was found by Heurico 1.16 in 3.62e-008 seconds.