The generator matrix

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

generates a code of length 39 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+168x^102+192x^103+315x^104+540x^105+1476x^106+924x^107+909x^108+1344x^109+3912x^110+1788x^111+1482x^112+2292x^113+6264x^114+2664x^115+3054x^116+3312x^117+9576x^118+3720x^119+2724x^120+3156x^121+7140x^122+2364x^123+1425x^124+1488x^125+2184x^126+636x^127+189x^128+156x^129+75x^132+33x^136+6x^140+24x^144+3x^148

The gray image is a linear code over GF(4) with n=156, k=8 and d=102.
This code was found by Heurico 1.16 in 10.8 seconds.