The generator matrix

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

generates a code of length 22 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+123x^48+60x^51+270x^52+144x^54+612x^55+417x^56+1728x^58+2520x^59+489x^60+7776x^62+5832x^63+609x^64+15552x^66+8748x^67+735x^68+11664x^70+6804x^71+744x^72+447x^76+183x^80+75x^84+3x^88

The gray image is a linear code over GF(4) with n=88, k=8 and d=48.
This code was found by Heurico 1.16 in 5.01 seconds.