The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+28x^33+84x^34+6x^36+4x^38+1x^40+4x^41

The gray image is a code over GF(2) with n=272, k=7 and d=132.
This code was found by Heurico 1.16 in 1.05e-007 seconds.