The generator matrix

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

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+192x^8+384x^9+904x^10+384x^11+172x^12+8x^14+3x^16

The gray image is a linear code over GF(2) with n=80, k=11 and d=32.
As d=35 is an upper bound for linear (80,11,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 11.
This code was found by Heurico 1.16 in 0.219 seconds.