The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+294x^29+1691x^30+4270x^31+8931x^32+15940x^33+20491x^34+26830x^35+21674x^36+16736x^37+8585x^38+3506x^39+1450x^40+468x^41+145x^42+50x^43+6x^44+2x^45+2x^48

The gray image is a code over GF(2) with n=280, k=17 and d=116.
This code was found by Heurico 1.16 in 61.5 seconds.