The generator matrix

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

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+456x^8+592x^9+2032x^10+544x^11+452x^12+16x^13+3x^16

The gray image is a linear code over GF(2) with n=80, k=12 and d=32.
As d=34 is an upper bound for linear (80,12,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 12.
This code was found by Heurico 1.16 in 145 seconds.