The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  1  X  X X+2  0  1  1  0  X  1  2  X  2  1  1  1  1 X+2  1  1 X+2  0  1 X+2  1  2  1  0  1  1  X
 0  1  0  0  0  0  1  3  1  2 X+1  3  1 X+2  1  X  3  3  1  0 X+2  1  1  1  2 X+3 X+3  3  1  3  0  1  X  0  X X+1  0 X+2  1  X X+1  X
 0  0  1  0  0  1  1  2  3  3 X+1 X+2  X  1 X+3  1 X+3 X+2  0  1  X  X X+1  3 X+1  1  3  X  1 X+3  3  2  0 X+1  1 X+2  1 X+2  X  X  0  1
 0  0  0  1 X+1 X+3  2 X+3 X+3  X X+1 X+2  3 X+1  0 X+2 X+2  0  3  1 X+3  2 X+2  X  3  0  1  1  X  2  1  2  1 X+2 X+2 X+2 X+2 X+3  X  2 X+1  3
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  2  0  2  2  0  0  0  0  0  2  2  0  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+190x^35+434x^36+812x^37+1063x^38+1408x^39+1492x^40+1946x^41+1770x^42+1930x^43+1474x^44+1538x^45+972x^46+646x^47+395x^48+174x^49+62x^50+48x^51+12x^52+10x^53+5x^54+2x^55

The gray image is a code over GF(2) with n=168, k=14 and d=70.
This code was found by Heurico 1.16 in 6.74 seconds.