The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+44x^37+78x^38+104x^39+140x^40+108x^41+112x^42+128x^43+96x^44+84x^45+58x^46+24x^47+18x^48+20x^49+6x^50+2x^58+1x^64

The gray image is a code over GF(2) with n=168, k=10 and d=74.
This code was found by Heurico 1.16 in 0.0717 seconds.