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  X  0  1  1  1  X  0  1  1  1  1  1  X  X
 0  X  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  X  0 X+2  2 X+2  0  2 X+2  X  X  0  0  2  2  0  2 X+2  X X+2  X  X X+2  X X+2 X+2 X+2  X X+2  0  0
 0  0  2  0  0  0  0  0  2  0  0  2  2  2  0  2  0  0  0  2  2  0  0  2  2  0  0  0  2  2  0  2  0  0  2  2  0  2  2  0  2  0
 0  0  0  2  0  0  0  2  0  0  0  2  0  0  2  0  2  2  2  0  0  2  0  2  2  2  2  0  2  0  2  2  0  0  0  2  0  2  0  0  2  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  2  2  0  2  0  2  2  2  0  0  2  0  0  2  0  2  0  0  2  0  0  2  0  2  2  2  0  0
 0  0  0  0  0  2  0  2  0  2  2  0  0  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  2  2  0  2  0  2  0  0  0  0
 0  0  0  0  0  0  2  0  2  0  2  0  0  0  2  0  2  2  0  2  0  2  2  2  0  2  2  0  0  2  2  0  0  2  0  0  2  2  2  2  2  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+88x^36+52x^38+199x^40+320x^42+234x^44+68x^46+47x^48+8x^50+6x^52+1x^72

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 0.081 seconds.