The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  X  X  1  X  1  0  X  1  1  1  1  0  X  X  0  X  X  X  0  0  0
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  X  X  X  X  X  X  0  0  0  X  0  0  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  X  X  X  X  X  X  0  X  0  X  X  X  X  X  X  X  X  X  X  X  0  0  X  X
 0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  X  0  X  0  X  0  X  0  X  X  X  0  X  0  X  X  X  0  X
 0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  X  0  X  0  0  X  X  0  X  X  0  0
 0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  0  X  X  0  0  X  0  X  X  0  0  X  X  X  X  X  0  0  0  0  X  X  X  X  X  X  0  X

generates a code of length 74 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+93x^72+30x^80+3x^88+1x^112

The gray image is a linear code over GF(2) with n=148, k=7 and d=72.
As d=72 is an upper bound for linear (148,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 65.7 seconds.