The generator matrix

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

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+196x^30+698x^31+1640x^32+2808x^33+4953x^34+7036x^35+10205x^36+13526x^37+15386x^38+17134x^39+16058x^40+13946x^41+10838x^42+7198x^43+4610x^44+2426x^45+1280x^46+632x^47+309x^48+126x^49+49x^50+6x^51+9x^52+2x^54

The gray image is a code over GF(2) with n=156, k=17 and d=60.
This code was found by Heurico 1.13 in 112 seconds.