The generator matrix

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

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+18x^33+85x^34+18x^35+2x^37+2x^39+1x^42+1x^44

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 0.015 seconds.