The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+1x^34+66x^35+44x^36+30x^37+46x^38+62x^39+2x^40+2x^41+1x^50+1x^56

The gray image is a code over GF(2) with n=148, k=8 and d=68.
This code was found by Heurico 1.16 in 0.0156 seconds.