The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+120x^35+61x^36+224x^37+96x^38+160x^39+43x^40+120x^41+16x^42+104x^43+33x^44+32x^45+4x^48+8x^49+2x^52

The gray image is a code over GF(2) with n=156, k=10 and d=70.
This code was found by Heurico 1.16 in 1.01 seconds.