The generator matrix

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

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+40x^29+101x^30+146x^31+221x^32+342x^33+394x^34+332x^35+217x^36+120x^37+70x^38+26x^39+6x^40+6x^41+10x^42+8x^43+2x^44+4x^45+1x^46+1x^52

The gray image is a code over GF(2) with n=272, k=11 and d=116.
This code was found by Heurico 1.16 in 0.079 seconds.