The generator matrix

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

generates a code of length 28 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+636x^69+360x^70+396x^71+1461x^72+3612x^73+2040x^74+2256x^75+5352x^76+11088x^77+5484x^78+7224x^79+14250x^80+24264x^81+12048x^82+13824x^83+25767x^84+36204x^85+14592x^86+14940x^87+20592x^88+23580x^89+7896x^90+4368x^91+4077x^92+5064x^93+588x^94+129x^96+33x^100+15x^104+3x^108

The gray image is a linear code over GF(4) with n=112, k=9 and d=69.
This code was found by Heurico 1.16 in 626 seconds.