The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+56x^30+16x^31+65x^32+256x^33+292x^34+208x^35+40x^36+32x^37+32x^38+21x^40+4x^42+1x^56

The gray image is a code over GF(2) with n=272, k=10 and d=120.
This code was found by Heurico 1.16 in 0.031 seconds.