The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+408x^32+635x^36+630x^40+318x^44+49x^48+7x^52

The gray image is a linear code over GF(2) with n=76, k=11 and d=32.
As d=32 is an upper bound for linear (76,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.10 in 712 seconds.