The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+66x^35+211x^36+368x^37+622x^38+684x^39+731x^40+940x^41+974x^42+976x^43+809x^44+664x^45+508x^46+290x^47+180x^48+70x^49+38x^50+26x^51+20x^52+4x^53+2x^54+6x^55+2x^57

The gray image is a code over GF(2) with n=168, k=13 and d=70.
This code was found by Heurico 1.16 in 1.98 seconds.