The generator matrix

 1  0  1  1  1 2X 3X+2  1  1  1  1 2X+2  1  1 X+2  1  1  X  1  1  2  1  1 3X  1  1  0  1  X  1  0  1  X  1
 0  1 X+1 X+2 2X+3  1  1 3X+2 X+1  X 3X+3  1 2X  3  1 2X+2  1  1  2 X+3  1 3X 2X+1  1 2X X+2  0  2 X+2 2X+1  X 3X+1 3X 2X+2
 0  0 2X+2  2 2X 2X+2  0  0 2X 2X+2  2  2 2X+2 2X+2 2X+2  2  2  2  0 2X  0  0 2X  0  2 2X+2 2X+2 2X 2X  0  2 2X 2X  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+270x^32+216x^33+212x^34+88x^35+107x^36+72x^37+44x^38+8x^39+3x^40+1x^44+2x^48

The gray image is a code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 0.734 seconds.