The generator matrix

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

generates a code of length 17 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+7x^16+110x^17+8x^18+2x^25

The gray image is a linear code over GF(2) with n=136, k=7 and d=64.
As d=66 is an upper bound for linear (136,7,2)-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.