The generator matrix

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

generates a code of length 27 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+468x^69+756x^70+168x^71+1302x^72+1980x^73+1776x^74+948x^75+3195x^76+4956x^77+3960x^78+1620x^79+5133x^80+8412x^81+5616x^82+2460x^83+6345x^84+7200x^85+4020x^86+948x^87+1896x^88+1560x^89+768x^90+33x^92+12x^96+3x^100

The gray image is a linear code over GF(4) with n=108, k=8 and d=69.
This code was found by Heurico 1.16 in 6.21 seconds.