The generator matrix

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

generates a code of length 37 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+165x^96+204x^97+132x^98+600x^99+1467x^100+912x^101+216x^102+2172x^103+3039x^104+2232x^105+576x^106+3936x^107+5517x^108+4080x^109+720x^110+6792x^111+7368x^112+4236x^113+804x^114+5928x^115+6105x^116+2976x^117+504x^118+2076x^119+1785x^120+720x^121+120x^122+72x^124+36x^128+30x^132+6x^136+9x^140

The gray image is a linear code over GF(4) with n=148, k=8 and d=96.
This code was found by Heurico 1.16 in 9.99 seconds.