The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+154x^26+580x^27+1378x^28+2648x^29+4662x^30+7164x^31+10247x^32+13546x^33+16204x^34+17398x^35+16318x^36+13972x^37+10721x^38+7186x^39+4380x^40+2460x^41+1201x^42+502x^43+220x^44+76x^45+49x^46+2x^47+2x^49+1x^50

The gray image is a code over GF(2) with n=140, k=17 and d=52.
This code was found by Heurico 1.13 in 94.4 seconds.