The generator matrix

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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+528x^139+660x^140+948x^141+972x^142+2028x^143+1707x^144+1884x^145+1872x^146+3348x^147+2754x^148+2700x^149+2376x^150+4332x^151+3663x^152+3720x^153+2952x^154+5184x^155+3942x^156+3588x^157+2532x^158+3948x^159+2754x^160+1860x^161+1320x^162+1884x^163+798x^164+636x^165+264x^166+252x^167+93x^168+24x^169+6x^172+6x^176

The gray image is a linear code over GF(4) with n=204, k=8 and d=139.
This code was found by Heurico 1.16 in 77.6 seconds.