The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+98x^28+342x^29+655x^30+928x^31+1388x^32+1788x^33+1883x^34+2144x^35+2096x^36+1726x^37+1370x^38+908x^39+559x^40+312x^41+123x^42+32x^43+16x^44+8x^45+1x^46+4x^47+2x^48

The gray image is a code over GF(2) with n=140, k=14 and d=56.
This code was found by Heurico 1.13 in 1.96 seconds.