The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  X  1  1  X  1  1  1  1  X  1  X  1  0  1  1  0  1  1  X  1  1  X  1  1  0  1  1  X  1  1
 0  1  1  0  1  1 X+1  0  1  0 X+1  1  X X+1  1  X  1  1  0  X  X X+1  1  1  1 X+1  1  0 X+1  1  X  1  1  X  1  1  0 X+1  1  X  1  1  0 X+1
 0  0  X  0  0  0  0  X  X  X  X  X  X  0  X  X  0  X  0  0  0  X  0  X  0  0  0  X  X  X  X  X  X  0  0  0  0  0  X  0  0  X  X  X
 0  0  0  X  0  X  X  X  X  0  X  0  0  0  0  X  X  X  0  X  0  0  X  X  0  0  X  X  X  0  X  X  0  0  0  X  X  X  X  X  X  X  0  0
 0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  X  0  X  0  0  X  0  X  0  X  X  0  0  X  0  0  0  X

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+14x^42+32x^43+39x^44+32x^45+7x^48+2x^58+1x^60

The gray image is a linear code over GF(2) with n=88, k=7 and d=42.
As d=42 is an upper bound for linear (88,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.0694 seconds.