The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+324x^29+1091x^30+2452x^31+3625x^32+5780x^33+6059x^34+6152x^35+3741x^36+2152x^37+851x^38+400x^39+108x^40+16x^41+5x^42+4x^43+5x^44+2x^46

The gray image is a code over GF(2) with n=272, k=15 and d=116.
This code was found by Heurico 1.16 in 4.47 seconds.