The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+102x^34+120x^35+322x^36+164x^37+257x^38+208x^39+243x^40+168x^41+220x^42+88x^43+81x^44+20x^45+22x^46+24x^48+6x^50+1x^52+1x^54

The gray image is a code over GF(2) with n=156, k=11 and d=68.
This code was found by Heurico 1.16 in 0.136 seconds.