The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+41x^36+108x^38+267x^40+128x^41+154x^42+28x^44+128x^45+72x^46+76x^48+18x^50+2x^52+1x^76

The gray image is a code over GF(2) with n=168, k=10 and d=72.
This code was found by Heurico 1.16 in 0.0761 seconds.