The generator matrix

 1  0  0  1  1  1  0  0  1  1  2  1  1  0  2 X+2  1  1  1  X  1  1  1  1  1  1  1 X+2  1 X+2  1  1 X+2  1  X  2 X+2  2  1
 0  1  0  0  1  1  1  2  1  0  1  X X+1  1  X  1  3  X X+3  1  2  X X+2 X+3 X+2  3  2  2  0  1 X+1 X+2  1  1  1  1  1  1  0
 0  0  1  1  0  3  1  1  0  2  1  1  1  X  1  X X+1 X+3  0  1  X X+3  2  X  1  X X+1  1 X+3  0 X+1 X+3 X+1  X X+2 X+1  0  1  1
 0  0  0  X  2  X  X X+2 X+2 X+2  0  0  2 X+2  2  0  X X+2  2  2 X+2  2  0  0  X  2  0  2  X  0  X  0 X+2 X+2  X  0  X  X  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+34x^34+196x^35+196x^36+330x^37+197x^38+322x^39+165x^40+240x^41+62x^42+126x^43+84x^44+52x^45+25x^46+8x^47+2x^50+2x^51+2x^52+2x^53+2x^55

The gray image is a code over GF(2) with n=156, k=11 and d=68.
This code was found by Heurico 1.11 in 0.0562 seconds.