The generator matrix

 1  1  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  1  1  1  1  1  1  1  1  X  X
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  2  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0  2  2  2  0  2  0  0  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  0  2  2  2  2  2  2  0  0  2  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  2  2  2  2  0  2  2  0  2  0  0  0  0  0  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  0  2  2  0  2  0  2  2  0  0  2  0  0  0  2  0  2  2  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  0  2  0  0  0  0  2  0  2  0  2  2  2  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  0  0  2  2  0  2  2  2  2  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  0  2  0  2  0  0  2  0  2  2  0  2  2  2  2  0  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  2  0  0  0  0  0  2  2  0  0  2  2  2  0  2  2
 0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  2  2  0  2  2  0  0  0  2  0  2  2  2  0  0  2  2  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+146x^28+356x^32+658x^36+768x^38+4096x^39+1200x^40+256x^42+430x^44+231x^48+46x^52+3x^56+1x^72

The gray image is a code over GF(2) with n=156, k=13 and d=56.
This code was found by Heurico 1.16 in 3.22 seconds.