The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+74x^27+843x^28+3002x^29+7855x^30+16908x^31+31108x^32+45132x^33+51627x^34+45566x^35+31911x^36+17114x^37+7325x^38+2480x^39+863x^40+248x^41+41x^42+28x^43+10x^44+8x^45

The gray image is a code over GF(2) with n=272, k=18 and d=108.
This code was found by Heurico 1.16 in 232 seconds.