The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  X  0  X  0  X  2  X  2  X  2  X  2  1  1  1  1  1  1  1
 0  X  0 X+2  0 X+2  0  X  2 X+2  2  X  2 X+2  2  X X+2  X X+2  X X+2  X X+2  X  X  X  X  X  X  X  X  X  0  0  0  2  0  2  2
 0  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  2  2  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  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+14x^38+96x^39+14x^40+1x^46+1x^48+1x^62

The gray image is a code over GF(2) with n=156, k=7 and d=76.
This code was found by Heurico 1.16 in 0.135 seconds.