The generator matrix

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

generates a code of length 24 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+207x^56+24x^57+60x^58+501x^60+360x^61+420x^62+1617x^64+2160x^65+1560x^66+5763x^68+6480x^69+3720x^70+10986x^72+9720x^73+4332x^74+8487x^76+5832x^77+2196x^78+642x^80+309x^84+147x^88+12x^92

The gray image is a linear code over GF(4) with n=96, k=8 and d=56.
This code was found by Heurico 1.16 in 13.9 seconds.