The generator matrix

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

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+318x^72+48x^73+48x^75+990x^76+288x^77+432x^79+1815x^80+768x^81+1296x^83+3465x^84+1248x^85+1296x^87+2799x^88+720x^89+687x^92+96x^96+39x^100+27x^104+3x^108

The gray image is a linear code over GF(4) with n=112, k=7 and d=72.
This code was found by Heurico 1.16 in 0.615 seconds.