The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  X  X  X  X  2  2  1  1  X  X  1  1  1  1  1  1  1  1  1
 0  X  0 X+2  2 X+2  2  X  0 X+2  0 X+2  2  X  2  X X+2  X X+2  X  0  2  X  X  X  X  0  2  0  2  0  2 X+2 X+2  X  X  0  0  2
 0  0  2  2  2  0  0  2  0  0  2  2  2  2  0  0  0  2  2  0  2  2  2  0  2  0  0  0  0  0  2  2  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+6x^38+44x^39+7x^40+4x^43+1x^46+1x^54

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 0.0218 seconds.