The generator matrix

 1  0  0  0  0  1  1  1  1 X+2  1  0  1  2  X  1  1  2  0  1  1  2  1  1  X X+2  1  1  0  1  2  X  1 X+2  0  0 X+2  1  1
 0  1  0  0  0  0  2  2  0  0  0  2 X+2  X  1  1  1  1  1 X+3  3  1  3 X+1  1  1  X  0  1 X+2  1  2 X+2  1  1  1 X+2 X+3  2
 0  0  1  0  0  0  3 X+1  2  1  1  1  2  2 X+1  1  X X+2 X+3 X+3  2  1 X+1  0  X X+2 X+3  3 X+1  X X+2  0  3  0  1  0  X  3  2
 0  0  0  1  0  1  1  X X+2  X  2  1  3  1  3 X+1  X  0  3 X+2 X+3  0 X+1  2 X+1  3 X+3  2 X+2  0 X+1  2  0  0  3  X  1  0  2
 0  0  0  0  1  1  2  0 X+3 X+1  1  1 X+2  3  0 X+1  3 X+1  1  X  0  1  X  2  0 X+1  1 X+3 X+2  1  3  1  2  X X+2 X+1  2 X+2 X+2
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  0  2  2  0  2  0  2  0  2  0  2  0  2  0  2  2  2  0  0  2  0  2

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+300x^31+840x^32+1522x^33+2505x^34+3846x^35+5144x^36+6400x^37+7696x^38+8284x^39+8144x^40+7084x^41+5334x^42+3710x^43+2318x^44+1200x^45+640x^46+366x^47+127x^48+50x^49+17x^50+4x^51+2x^52+2x^55

The gray image is a code over GF(2) with n=156, k=16 and d=62.
This code was found by Heurico 1.13 in 39 seconds.