The generator matrix

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

generates a code of length 19 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+54x^44+156x^48+174x^52+177x^56+3072x^57+177x^60+141x^64+120x^68+21x^72+3x^76

The gray image is a linear code over GF(4) with n=76, k=6 and d=44.
This code was found by Heurico 1.16 in 0.0383 seconds.