The generator matrix

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

generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+159x^72+168x^75+345x^76+1080x^79+1014x^80+4512x^83+1911x^84+12720x^87+4326x^88+18216x^91+4947x^92+11544x^95+2775x^96+912x^99+465x^100+303x^104+108x^108+30x^112

The gray image is a linear code over GF(4) with n=120, k=8 and d=72.
This code was found by Heurico 1.16 in 8.31 seconds.