The generator matrix

 1  0  0  1  1  1  X  2  1  0  1  1  1 X+2  1  1  2  1  2  1  1  2  1 X+2 X+2  1  X  2  1  1  2  1  0 X+2  X
 0  1  0  1  0 X+3  1  X X+1  1  X X+2 X+3  1 X+1 X+2  1  3  1 X+2 X+2  1 X+1  X  1  2  1  0 X+2  0  1  1  1  X  1
 0  0  1  1  1  0  1  1 X+3 X+2  X  1 X+2  1  2 X+1 X+3 X+1  0  X  X  2  X  1 X+3 X+2 X+2  1 X+3  X X+2 X+3  X  1  3
 0  0  0  X  0 X+2  2  X  0 X+2 X+2 X+2  2  0  X  X X+2  X  0  2  X X+2  2  X  2  X  0 X+2  2  X  2  X X+2  0  0
 0  0  0  0  X  0  2 X+2 X+2  X  X  2  X X+2 X+2  X  2  X X+2 X+2  2  0  0  0 X+2  0  X  X  2  2  X  2 X+2  X  0
 0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  2  0  2  2  0  0  0  2  0  2  0  2  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+186x^28+180x^29+792x^30+820x^31+1502x^32+1436x^33+2114x^34+2200x^35+2253x^36+1632x^37+1418x^38+740x^39+686x^40+140x^41+214x^42+16x^43+40x^44+4x^45+6x^46+3x^48+1x^52

The gray image is a code over GF(2) with n=140, k=14 and d=56.
This code was found by Heurico 1.16 in 5.55 seconds.