The generator matrix

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

generates a code of length 23 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+273x^56+240x^57+168x^58+780x^59+972x^60+1332x^61+768x^62+1680x^63+3048x^64+4320x^65+2448x^66+4680x^67+6549x^68+8520x^69+3648x^70+5520x^71+6774x^72+6480x^73+2184x^74+2700x^75+1686x^76+612x^77+81x^80+57x^84+15x^88

The gray image is a linear code over GF(4) with n=92, k=8 and d=56.
This code was found by Heurico 1.16 in 5.29 seconds.