The generator matrix

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

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+68x^34+154x^35+151x^36+426x^37+208x^38+246x^39+149x^40+252x^41+86x^42+136x^43+71x^44+58x^45+20x^46+6x^47+10x^48+2x^50+2x^51+2x^52

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 0.108 seconds.