The generator matrix

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

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+75x^56+36x^57+48x^58+156x^59+162x^60+432x^61+288x^62+336x^63+177x^64+1944x^65+768x^66+936x^67+153x^68+3888x^69+1248x^70+1104x^71+141x^72+2916x^73+720x^74+540x^75+156x^76+96x^80+57x^84+6x^88

The gray image is a linear code over GF(4) with n=92, k=7 and d=56.
This code was found by Heurico 1.16 in 0.4 seconds.