The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  0  1  1  1 a^2*X  1 a^2*X  1  1  1  1  1 a*X  1 a*X  1  1 a*X  1  1  0  1  1  1  1  1  1  1  0  1  X  1  1  1  1  1 a*X  1
 0  1  0  1  a a^2 a^2*X a^2*X  1 a^2 a^2*X+1 a^2*X+a^2  a  1 a^2*X+a^2 a^2*X+a a*X+1  1 a*X+a  1  0 a^2*X+a a^2*X+a  0 a^2*X  1 a^2*X+1  1  1 X+a^2  1 X+a^2 X+1  1  1 a*X+a^2 a*X+a^2 X+a  1 a^2*X a*X+a  1  X  1 X+a a*X X+a a*X a*X+1  1  0
 0  0  1 a^2  a  1  1 a^2 X+1 a^2  0  0  X  a X+a X+a^2 a*X+a  1 a^2*X+1 a^2 X+a a*X+a a^2*X a^2*X+a  1 X+1 X+1 X+a^2  a a^2*X+1 a*X+a^2 a*X+a^2 a^2*X+1  0 X+1  a  1 a*X a*X X+a^2 a*X+a^2 a^2 a^2  X X+1 X+a  0 X+a a*X+a a*X+a  0
 0  0  0  X  0  X  0  0 a^2*X a^2*X a*X a*X a^2*X  X  0 a^2*X  X  0 a*X a^2*X a*X  X  0 a^2*X  X  0 a*X a*X  X a^2*X  0  0 a*X  X a^2*X  X  X a*X a*X a^2*X  0 a^2*X a*X  X  X  0 a*X a*X  0 a^2*X  0
 0  0  0  0  X a^2*X a*X a^2*X  X  0  0  X a*X a^2*X a^2*X a^2*X a*X  X a*X  X a*X a^2*X a*X  X a*X  0 a^2*X a*X  X a*X a*X  X  X a*X a^2*X a*X  0  X a^2*X a*X  0  0  X  X  X  X  0  0 a^2*X  0 a^2*X

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+141x^136+192x^137+396x^139+1020x^140+1008x^141+192x^142+1524x^143+2643x^144+2412x^145+348x^146+2316x^147+4194x^148+3588x^149+672x^150+2928x^151+5970x^152+5832x^153+888x^154+3780x^155+5793x^156+5256x^157+768x^158+2964x^159+4269x^160+2700x^161+204x^162+1284x^163+1278x^164+516x^165+168x^167+192x^168+33x^172+39x^176+18x^180+3x^184+6x^192

The gray image is a linear code over GF(4) with n=204, k=8 and d=136.
This code was found by Heurico 1.16 in 14.2 seconds.