The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+70x^28+189x^32+48x^34+364x^36+304x^38+2048x^39+533x^40+144x^42+230x^44+16x^46+105x^48+40x^52+3x^56+1x^64

The gray image is a code over GF(2) with n=156, k=12 and d=56.
This code was found by Heurico 1.16 in 0.778 seconds.