The generator matrix

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

generates a code of length 28 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+180x^70+144x^71+402x^72+240x^73+1332x^74+780x^75+1140x^76+960x^77+4068x^78+2016x^79+1758x^80+3360x^81+8808x^82+3960x^83+3081x^84+4800x^85+10332x^86+3696x^87+2700x^88+2928x^89+5700x^90+1692x^91+1005x^92+300x^94+81x^96+51x^100+18x^104+3x^108

The gray image is a linear code over GF(4) with n=112, k=8 and d=70.
This code was found by Heurico 1.16 in 8.91 seconds.