The generator matrix

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

generates a code of length 28 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+840x^75+420x^76+2388x^79+996x^80+3636x^83+1221x^84+3708x^87+1128x^88+1716x^91+273x^92+51x^96+3x^100+3x^108

The gray image is a linear code over GF(4) with n=112, k=7 and d=75.
This code was found by Heurico 1.16 in 36.7 seconds.