The generator matrix

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

generates a code of length 22 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+222x^56+156x^57+96x^58+420x^59+1257x^60+648x^61+288x^62+660x^63+2622x^64+864x^65+672x^66+1260x^67+3201x^68+1080x^69+480x^70+732x^71+1356x^72+324x^73+27x^76+15x^80+3x^84

The gray image is a linear code over GF(4) with n=88, k=7 and d=56.
This code was found by Heurico 1.16 in 0.247 seconds.