The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1
 0  2  0  0  0  2  2  2  0  0  0  2  0  2  2  2  0  0  2  2  0  2  2  0  0  0  2  0  2  2  2  0  0  0  0  2  0  2  2
 0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0  0  0  0  0  2  2  2  2  0
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0  0  0  2  2  0  0  2  2

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+7x^38+46x^39+7x^40+2x^47+1x^62

The gray image is a code over GF(2) with n=156, k=6 and d=76.
This code was found by Heurico 1.16 in 0.0164 seconds.