The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+62x^30+98x^31+237x^32+352x^33+626x^34+900x^35+1258x^36+1742x^37+1870x^38+2030x^39+2010x^40+1738x^41+1214x^42+902x^43+652x^44+306x^45+172x^46+96x^47+54x^48+22x^49+24x^50+6x^51+10x^52+2x^56

The gray image is a code over GF(2) with n=156, k=14 and d=60.
This code was found by Heurico 1.16 in 7.62 seconds.