The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  X  1  2  1  1  1  1  0  1  1 X+2  1  1 X+2  1  1  2  2  1  1  0  1 X+2  X  1  1  1  1  1  0  1  1  1  0 X+2  1  1  X X+2  1  1  1  1  X  1  1 X+2  1  X  2  1  1  1  1 X+2  0  1  1  X  X  1  1  1  1  1  X  0  2  1 X+2  1  1  2  1  0  0  1  1  X
 0  1  1 X+2 X+3  1  0 X+1  1  X  1  3  1  0 X+3  2 X+3  1 X+2  1  1 X+2  1  1  0  0  1  1 X+1 X+1  1  3  1  1  2 X+2  3 X+3 X+3  1  1  X  2  1  1 X+2  2  1  1 X+3  1 X+2  3  1  X  2  1  3  1  1  1  3 X+3 X+1  1  1  1 X+1  1  1  0 X+1  2 X+3 X+2  1  1  2 X+2  1  0  2  1 X+3  X  X  2  0  2
 0  0  X  0 X+2  0 X+2  0 X+2 X+2  X  2  X  2  X  X  2  2  X X+2  2  2  0 X+2  0  0  X  X  0  0  0  2  2  2  X  0  2  X  X  2  X  X X+2  0  2  2  2  X  2  X X+2  2 X+2 X+2  X  0  0  0 X+2 X+2  X  X X+2 X+2  X  2  0  0  2  0  0  2 X+2 X+2 X+2  2 X+2  X  0  0  0  0  X  0 X+2 X+2  X  0  X
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  2  0  0  2  2  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  2  2  0  2  0  2  2  2  0  0  2  2  0  2  2  0  0  2  0  2  2  2  0  0  0  0  2  0  2  0  0  2  2  0  0  0  2  2  0  0  0  2  2
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  2  0  2  0  0  2  2  0  0  2  0  2  2  0  0  2  0  2  2  0  2  0  2  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  2  2  0  0  0  0  0  0  2  0  2  2  2  0  0  0  0  0  2  0  2  2  2  0  0  2  0  0  0  2  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  2  2  0  0  2  0  2  0  0  2  2  0  2  0  2  2  0  2  0  0  2  2  2  0  2  0  0  0  2  0  2  0  2  0  2  0  0  2  2  0  0  2  0  0  2  0  0  2  2  0  2  0  0  2  0  0  2  0  0  0  2  2  0  0  0  2  2  2
 0  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  0  2  0  0  0  2  2  2  2  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  2  2  2  0  0  2  2  0  2  0  2  0  2  0  2  0  2  0  0  0  0  0  0  0  2  2  2  0  2  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  2  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  0  2  2  2  0  0  2  2  2  2  0  2  2  2  2  2  0  2  2  0  2  0  2  0  0  2  2  0  2  0  2  2  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+32x^77+101x^78+140x^79+304x^80+386x^81+438x^82+628x^83+799x^84+1026x^85+1186x^86+1212x^87+1261x^88+1356x^89+1344x^90+1326x^91+1197x^92+914x^93+798x^94+640x^95+407x^96+318x^97+175x^98+124x^99+92x^100+42x^101+35x^102+24x^103+21x^104+20x^105+10x^106+2x^107+5x^108+2x^109+7x^110+6x^112+1x^114+3x^116+1x^118

The gray image is a code over GF(2) with n=356, k=14 and d=154.
This code was found by Heurico 1.16 in 35.5 seconds.