The generator matrix

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

generates a code of length 28 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+573x^72+648x^73+492x^74+996x^75+2283x^76+1992x^77+1200x^78+2196x^79+5094x^80+3804x^81+2508x^82+4428x^83+8226x^84+5580x^85+3396x^86+4764x^87+7500x^88+4236x^89+1464x^90+1440x^91+1887x^92+636x^93+156x^94+21x^96+12x^100+3x^104

The gray image is a linear code over GF(4) with n=112, k=8 and d=72.
This code was found by Heurico 1.16 in 6.85 seconds.