The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+13x^32+72x^33+78x^34+80x^35+1x^36+8x^37+1x^38+1x^44+1x^46

The gray image is a code over GF(2) with n=272, k=8 and d=128.
This code was found by Heurico 1.16 in 0.015 seconds.