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

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

Homogenous weight enumerator: w(x)=1x^0+12x^38+96x^39+13x^40+2x^42+2x^44+1x^46+1x^54

The gray image is a code over GF(2) with n=312, k=7 and d=152.
This code was found by Heurico 1.16 in 0.032 seconds.