The generator matrix

 1  0  0  1  1  1  2  1  1  1  1 X+2  0  0  X  X  0  1  1  X  1  1  1  0  1  1  1  1 X+2  1  1  1 X+2  2  1
 0  1  0  1  X X+3  1  0 X+2  3 X+3  1  1  X  1  1  2  1 X+2  1  1 X+2  1 X+2  2  2 X+3 X+2  2  3 X+3  0  1  1  0
 0  0  1  1  1  0 X+1  X X+3 X+1  X  0 X+1  1  2 X+1  1  0  X  X  1 X+1  0  1  2  1  0  3  1  1  3 X+2  2 X+2  0
 0  0  0  X  0 X+2  X X+2 X+2  2  2  0  2 X+2 X+2 X+2 X+2  X  X  X  0  0  2  2  0  2  2 X+2 X+2 X+2  X X+2 X+2 X+2  0
 0  0  0  0  2  0  2  0  2  0  0  2  2  0  2  0  0  2  0  0  2  0  2  2  0  0  2  2  2  0  2  2  0  2  0
 0  0  0  0  0  2  0  0  0  0  2  2  0  0  0  0  2  2  2  0  2  2  2  2  2  0  0  2  2  2  0  2  0  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+49x^28+150x^29+386x^30+506x^31+670x^32+848x^33+960x^34+1080x^35+926x^36+932x^37+732x^38+420x^39+254x^40+112x^41+96x^42+40x^43+17x^44+6x^45+2x^46+2x^47+3x^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 1.48 seconds.