The generator matrix

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

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+46x^10+32x^11+46x^12+2x^14+1x^16

The gray image is a linear code over GF(2) with n=88, k=7 and d=40.
As d=42 is an upper bound for linear (88,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in 3.62e-008 seconds.