The generator matrix

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

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+77x^28+48x^30+300x^32+390x^34+128x^35+944x^36+512x^37+1256x^38+768x^39+1474x^40+512x^41+740x^42+128x^43+608x^44+120x^46+141x^48+6x^50+33x^52+4x^56+1x^60+1x^68

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 2.62 seconds.