The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+50x^36+224x^37+154x^38+544x^39+107x^40+544x^41+148x^42+224x^43+44x^44+2x^46+3x^48+2x^52+1x^56

The gray image is a code over GF(2) with n=320, k=11 and d=144.
This code was found by Heurico 1.16 in 0.063 seconds.