The generator matrix

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

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+120x^28+72x^29+514x^30+316x^31+818x^32+732x^33+1142x^34+864x^35+1106x^36+672x^37+826x^38+348x^39+412x^40+60x^41+130x^42+8x^43+38x^44+12x^46+1x^48

The gray image is a code over GF(2) with n=140, k=13 and d=56.
This code was found by Heurico 1.16 in 1.85 seconds.