The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+99x^30+136x^31+286x^32+192x^33+646x^34+192x^35+286x^36+96x^37+66x^38+24x^39+19x^40+4x^42+1x^54

The gray image is a code over GF(2) with n=272, k=11 and d=120.
This code was found by Heurico 1.16 in 0.062 seconds.