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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+9x^38+16x^40+32x^41+143x^42+32x^43+12x^44+7x^46+3x^48+1x^82

The gray image is a code over GF(2) with n=168, k=8 and d=76.
This code was found by Heurico 1.16 in 0.0263 seconds.