The generator matrix

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

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+416x^32+614x^36+643x^40+324x^44+43x^48+6x^52+1x^56

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 1.16 in 8.24 seconds.