The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0 X+2  1  1  0  1 X+2  1  1  1  1  1  0  1  0  1 X+2 X+2  1  1  1  0  2  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1  1  3 X+1  1  3  1 X+2  0 X+2 X+1  3  1  0  1 X+2  1  1  0 X+1 X+1  1  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  2  2  2  2  0  2  0  0  2  2  2  2  2  0  2  2  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  2  0  0  0  2  2  0  0  0  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  0  2  2  2  2  0  0  2  0  0  2  0  0  2  2  0  2  0  2  2  0  0  0  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  0  0  2  0  2  2  2  0  2  0  2  0  2  0  2  0  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  0  2  2  2  0  2  2  2  2  2  0  2  2  2  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  0  2  0  0  0  0  2  0  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+36x^28+4x^29+70x^30+64x^31+217x^32+344x^33+415x^34+1088x^35+939x^36+2200x^37+1421x^38+2816x^39+1365x^40+2240x^41+942x^42+1088x^43+442x^44+324x^45+178x^46+64x^47+64x^48+8x^49+35x^50+7x^52+9x^54+1x^56+2x^62

The gray image is a code over GF(2) with n=156, k=14 and d=56.
This code was found by Heurico 1.16 in 6.36 seconds.