The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+397x^32+256x^34+352x^36+16x^40+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 0.031 seconds.