The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1 aX
 0  1  0  1  0 (a+1)X (a+1)X+a (a+1)X+1 (a+1)X+a  1  0 aX+1  X a+1 aX (a+1)X+1  a aX+1 (a+1)X  1
 0  0  1 a+1 a+1  1 X+a+1  0  1  1  a (a+1)X+a  1 X+1 X+1 (a+1)X+1  0 X+a X+1  1
 0  0  0  X  0  0 aX aX  X  0 aX  X (a+1)X  X aX (a+1)X (a+1)X  0 (a+1)X aX
 0  0  0  0 (a+1)X  X aX  0 (a+1)X (a+1)X  X aX  X  0 (a+1)X  0  X aX aX aX

generates a code of length 20 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+471x^48+216x^49+288x^50+192x^51+2259x^52+1056x^53+672x^54+1728x^55+6909x^56+3216x^57+2016x^58+5184x^59+13581x^60+4896x^61+2016x^62+5184x^63+10464x^64+2904x^65+1152x^66+1029x^68+75x^72+27x^76

The gray image is a linear code over GF(4) with n=80, k=8 and d=48.
This code was found by Heurico 1.16 in 4.77 seconds.